Lam Fung Academy· LF Academy
Primary 5 · Lesson 36 · Student Handout
SSPA Specialty - Geometry Questions Sprint for Full Score
T4 area + T5 volume/geometry · Two geometric traps total attack · 75 minutes · 1-to-3 Online Lesson
Corresponding textbooks:Scored test paper 1 + paper 2 geometry questions (accounting for about 25-35% of the paper) · Area · Volume · Combined figures
Core traps:🪤 T4 area formula trap · T5 geometry/volume trap —🔴 SSPA compulsory exam
SSPA association:🔴 High frequencyThe average score loss rate for geometry questions is 40%, formula confusion is the number one killer
Prerequisite knowledge:L3–L6 area (parallelogram · triangle · trapezoid · polygon)
Class goal:❶ Area formula muscle memory ❷ Zero confusion in volume calculations ❸ Combined graph segmentation strategies ❹ Correct unit conversion
Core traps:🪤 T4 area formula trap · T5 geometry/volume trap —🔴 SSPA compulsory exam
SSPA association:🔴 High frequencyThe average score loss rate for geometry questions is 40%, formula confusion is the number one killer
Prerequisite knowledge:L3–L6 area (parallelogram · triangle · trapezoid · polygon)
Class goal:❶ Area formula muscle memory ❷ Zero confusion in volume calculations ❸ Combined graph segmentation strategies ❹ Correct unit conversion
Student Name:
Class:
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Time Spent:
I. Geometry warm-up (total 5 questions, 5 minutes)
🏆 SSPA衝刺·限時挑戰
模擬真實SSPA考試！限時作答，每題計分。答對率達80%解鎖「SSPA戰士」勳章！
⚡ 開始模擬考 →
| # | Question | Difficulty | Working Space |
|---|---|---|---|
| W1 | Write the formula for the area of a parallelogram. | 🌱 | |
| W2 | Write the formula for the area of a triangle. | 🌱 | |
| W3 | Write the formula for the area of a trapezoid. | 🌱 | |
| W4 | The rectangle is 8 cm long and 5 cm wide. Area = ? Perimeter = ? | 🌱 | |
| W5 | The side length of the square is 6 cm. Area = ? Perimeter = ? | 🌱 |
📐 Quick reference for geometric figures (this Lesson has/haveQuestiontotaluse)
Square A=a²
P=4a
Rectangle A=l×w
P=2(l+w)
Triangle A=½bh
High hem
isosceles triangle
Both waists are equal and the height is on the inside
Trapezoid A=½(a+b)h
b₁=upper bottom·b₂=lower bottom
Circle A=πr²·C=2πr
π≈3.14 or 22/7
⚠️ The most common mistakes in SSPA geometry questions: ① Confusing the area formula and the perimeter formula ② Forgetting ÷2 (triangle/trapezoid) ③ The height must be the vertical distance ④ Wrong writing of the unit (cm² vs cm)
II.Core Knowledge + Worked Examples
Knowledge Point 1: Area Trap Total Attack (T4 Area Formula) 🔴 SSPA required test
Five major area formulas (Must have muscle memory!):
① Area of square = side length × side length
② Area of rectangle = length × width
③ Area of parallelogram = base ×Height(Height is the vertical distance, not the hypotenuse!)
④ Area of triangle = base × height÷ 2(÷2 is easiest to forget!)
⑤ Area of trapezoid =(upper base + lower base) × height ÷ 2(not "add height and multiply by 2"!)
Unit trap:The area unit is cm²/m², not cm/m! The answer must be written in square units!
① Area of square = side length × side length
② Area of rectangle = length × width
③ Area of parallelogram = base ×Height(Height is the vertical distance, not the hypotenuse!)
④ Area of triangle = base × height÷ 2(÷2 is easiest to forget!)
⑤ Area of trapezoid =(upper base + lower base) × height ÷ 2(not "add height and multiply by 2"!)
Unit trap:The area unit is cm²/m², not cm/m! The answer must be written in square units!
Figure 1: Trapezoid area = (upper base + lower base) × height ÷ 2
Example KP1-1: Trapezoid area formula trap
The upper base of the trapezoid is 6 cm, the lower base is 10 cm, and the height is 4 cm. Area = ?
❌ Common mistakes
(6+10+4) ÷ 2 = 10 cm²
Add more height! The formula is (upper bottom + lower bottom) × height ÷ 2
✅ Correct solution
(6+10)×4÷2 = 32 cm²
First add the two bases = 16, × height = 64, ÷2 = 32
Example KP1-2: Height of parallelogram vs hypotenuse
The base of a parallelogram is 8 cm, the height is 5 cm, and the hypotenuse is 6 cm. Area = ?
❌ Common mistakes
8 × 6 = 48 cm²
Used a bevel! Area of parallelogram = base × height (vertical distance)
✅ Correct solution
8 × 5 = 40 cm²
Height = vertical distance = 5 cm, not hypotenuse 6 cm
🧠 Tip: "Multiply the height of a flat base by multiplying it, divide a triangle by two, add two bases of a trapezoid, multiply the height by dividing by two, and use the hypotenuse as a trap."
⚠️ The three most common mistakes in T4: (1) Forgetting ÷2 for triangles (2) Using the hypotenuse for parallelograms (3) Recording the trapezoid formula as (upper base + lower base + height) × 2
KP1 Synchronization practice — areacalculate (question 1-15)
| # | Question | Difficulty | Working Space |
|---|---|---|---|
| 1 | The parallelogram has a base of 12 cm and a height of 7 cm. Area = ? | 🌱 | |
| 2 | Triangular base 10 cm, height 6 cm. Area = ? (Did you divide by 2?) | 🌱 | |
| 3 | The upper base of the trapezoid is 5 cm, the lower base is 9 cm, and the height is 6 cm. Area = ? | 🌱 | |
| 4 | The rectangle is 15 cm long and 8 cm wide. Area = ? Perimeter = ? | 🌱 | |
| 5 | The side length of the square is 9 cm. Area = ? | 🌱 | |
| 6 | The parallelogram has a base of 20 cm, a height of 8 cm, and a hypotenuse of 10 cm. Area = ? | 🌿 | |
| 7 | Triangular base 14 cm, height 9 cm. Area = ? | 🌿 | |
| 8 | The upper base of the trapezoid is 7 cm, the lower base is 13 cm, and the height is 5 cm. Area = ? | 🌿 | |
| 9 | The parallelogram has a base of 3.5 cm and a height of 2 cm. Area = ? | 🌿 | |
| 10 | The area of the triangle is 24 cm² and the base is 8 cm. How high is it? | 🌳 | |
| 11 | The area of a trapezoid is 40 cm², its upper base is 5 cm, and its lower base is 11 cm. How high is it? | 🌳 | |
| 12 | A parallelogram and a triangle have the same base and height. The area of the triangle is 18 cm². Area of parallelogram = ? | 🌳 | |
| 13 | The base of the triangle is 16 cm and the height is half the base. Area = ? | 🌳 | |
| 14 | A parallelogram has an area of 72 cm² and a height of 8 cm. bottom = ? (Note: not the hypotenuse!) | 🌳 | |
| 15 | Two identical trapezoids form a parallelogram. Each trapezoid has an upper base of 4 cm, a lower base of 10 cm, and a height of 6 cm. The area of the parallelogram = ? | 🌳 |
Knowledge Point 2: Volume Trap Total Attack (T5 Geometry/Volume) 🔴 SSPA required test
Core formulas and traps of volume:
① Volume of cuboid = length × width × height
② Volume of cube = side length × side length × side length (cube of side length)
③ Unit trap |||SEP|||: The volume unit is cm³/m³ (cubic), not cm² (square)!Capacity conversion
④ Surface area vs volume confusion |||SEP|||: Surface area = sum of the areas of all faces (unit cm²), volume = length × width × height (unit cm³)：1 cm³ = 1 mL，1000 cm³ = 1 L
⑤ Surface area vs volume confusion: Surface area = sum of the areas of all faces (unit cm²), volume = length × width × height (unit cm³)
① Volume of cuboid = length × width × height
② Volume of cube = side length × side length × side length (cube of side length)
③ Unit trap |||SEP|||: The volume unit is cm³/m³ (cubic), not cm² (square)!Capacity conversion
④ Surface area vs volume confusion |||SEP|||: Surface area = sum of the areas of all faces (unit cm²), volume = length × width × height (unit cm³)：1 cm³ = 1 mL，1000 cm³ = 1 L
⑤ Surface area vs volume confusion: Surface area = sum of the areas of all faces (unit cm²), volume = length × width × height (unit cm³)
Figure 2: Volume of cuboid = length × width × height (unit: cm³)
Example KP2-1: Volume vs surface area confusion
A cuboid is 5 cm long, 4 cm wide and 3 cm high. Find (a) volume (b) surface area.
❌ Common mistakes
Volume = surface area = 5×4=20
Confusing volume and surface area with wrong units
✅ Correct solution
Volume = 5×4×3 = 60 cm³
Surface area = 2(5×4+5×3+4×3)
= 2(20+15+12) = 94 cm²
Surface area = 2(5×4+5×3+4×3)
= 2(20+15+12) = 94 cm²
The volume is cubic (×3 times), and the surface area is the sum of the areas of the six sides
Example KP2-2: Capacity conversion trap
A water tank is 20 cm long, 15 cm wide and 10 cm high. How many liters of water can be filled?
❌ Common mistakes
20×15×10 = 3000 L
3000 cm³ ≠ 3000 L！1 L = 1000 cm³
✅ Correct solution
Volume = 20×15×10 = 3000 cm³
= 3000 ÷ 1000 = 3 L
= 3000 ÷ 1000 = 3 L
cm³ to L to ÷1000
⚠️ T5 must remember: 1 cm³ = 1 mL, 1000 cm³ = 1 L. The unit of volume is "cubic" not "square"!
KP2 synchronization practice — volume and table area (question 16-28)
| # | Question | Difficulty | Working Space |
|---|---|---|---|
| 16 | The cuboid is 6 cm long, 4 cm wide and 2 cm high. Volume = ? | 🌱 | |
| 17 | The side length of the cube is 5 cm. Volume = ? | 🌱 | |
| 18 | The cuboid is 10 cm long, 5 cm wide and 3 cm high. (a) Volume = ? (b) Surface area = ? | 🌿 | |
| 19 | The inside of the tank is 30 cm long, 20 cm wide, and 15 cm deep. Volume of water = ? How many liters? | 🌿 | |
| 20 | The surface area of the cube is 150 cm². Side length = ? Volume = ? | 🌳 | |
| 21 | The volume of a cuboid is 240 cm³, its length is 10 cm and its width is 6 cm. High = ? | 🌿 | |
| 22 | A fish tank is 40 cm long, 25 cm wide, and 30 cm high. How many liters of water can be filled? (1 L = 1000 cm³) | 🌿 | |
| 23 | The side length of the cube is 8 cm. Surface area = ? Volume = ? (Note that the units are different!) | 🌿 | |
| 24 | The sum of the lengths of all sides of a cuboid is 48 cm. 6 cm long, 4 cm wide. High = ? Volume = ? | 🌳 | |
| 25 | The volume of a cube is 512 cm³. Side length = ? Surface area = ? | 🌳 | |
| 26 | The original water in the water tank is 5 L. After a stone is placed, the water level rises and the volume becomes 5.8 L. What is the volume of the stone in cm³? | 🌳 | |
| 27 | The length of a cuboid is 8 cm, its width is half its length, and its height is twice its width. Volume = ? | 🏔️ | |
| 28 | Cut a cube with side length 10 cm into 8 identical small cubes. Volume of each small cube = ? Side length = ? | 🏔️ |
Knowledge Point 3: Combination Graphics Strategy (T4 + T5 Comprehensive) 🔴 SSPA Required Exam
Three-step method for solving combined graphics problems:
① Divide |||SEP|||: Split the combined graphics into basic graphics (rectangle, triangle, trapezoid, parallelogram)Mark the dimensions |||SEP|||: Mark the required base, height, length, and width for each basic graphics (note that some dimensions need to be calculated)
② Calculate separately and then merge: Add (merge graphics), subtract (hollow out graphics)
③ Volume combination: Divide into multiple cuboids/cubes first, find the volumes separately and then add them up
Overlap trap: When two graphics overlap, do not repeat calculations!
overlap trap: When two graphics overlap, do not repeat calculations!
① Divide |||SEP|||: Split the combined graphics into basic graphics (rectangle, triangle, trapezoid, parallelogram)Mark the dimensions |||SEP|||: Mark the required base, height, length, and width for each basic graphics (note that some dimensions need to be calculated)
② Calculate separately and then merge: Add (merge graphics), subtract (hollow out graphics)
③ Volume combination: Divide into multiple cuboids/cubes first, find the volumes separately and then add them up
Overlap trap: When two graphics overlap, do not repeat calculations!
overlap trap: When two graphics overlap, do not repeat calculations!
Figure 3: Combined shape = rectangle + triangle (division method)
Example question KP3-1: Area of combined graphics (refer to Figure 3)
Find the total area of the combined shapes in Figure 3. Rectangle 12×8, triangle base 10 and height 6.
❌ Common mistakes
12×8 + 10×6 = 96+60 = 156 cm²
Triangle Forgot ÷2!
✅ Correct solution
A = 12×8 = 96 cm²
B = 10×6÷2 = 30 cm²
Total = 126 cm²
B = 10×6÷2 = 30 cm²
Total = 126 cm²
Use the correct formula for each basic graph
Example KP3-2: Combined volume (superposition of two cuboids)
An L-shaped object consists of two cuboids: a lower cuboid 10×5×4 cm and an upper cuboid 6×5×3 cm stacked at the lower end. Total volume = ?
❌ Common mistakes
10×5×4 + 6×5×3 = 200+90 = 290 cm³
It seems correct, but if the two cuboids overlap, they need to be subtracted.
✅ Correct solution
V₁ = 10×5×4 = 200 cm³
V₂ = 6×5×3 = 90 cm³
Total = 290 cm³ (without overlap)
V₂ = 6×5×3 = 90 cm³
Total = 290 cm³ (without overlap)
Calculate the volumes separately and add them after confirming there is no overlap.
⚠️ The most frequent errors in combined graphics: (1) Forgetting ÷2 for triangles (2) Forgetting to calculate the "hidden size" (3) Repeating calculations for overlapping parts
KP3 synchronization practice — compound shape (question 29-40)
| # | Question | Difficulty | Working Space |
|---|---|---|---|
| 29 | A composite figure consists of a rectangle (8 × 5 cm) and a triangle (base 8 cm, height 4 cm). Total area = ? | 🌿 | |
| 30 | Cut out a triangle (base 6 cm, height 4 cm) in a rectangle (10×6 cm). Remaining area = ? | 🌿 | |
| 31 | A trapezoid (upper base 4 cm, lower base 10 cm, height 6 cm) is topped by a triangle (base 10 cm, height 3 cm). Total area = ? | 🌳 | |
| 32 | Two identical parallelograms (base 8 cm, height 5 cm) are put together to overlap a triangle (base 8 cm, height 2.5 cm). Total area = ? | 🌳 | |
| 33 | An L-shaped plane consists of two rectangles: 12×4 cm vertically and 8×5 cm horizontally. They overlap a 4 × 4 cm square. Total area = ? | 🏔️ | |
| 34 | A stair-shaped volume consists of 3 levels. Each level is 10 cm long, 5 cm wide and 2 cm high. Three levels are stacked to form a ladder. Total volume = ? | 🌳 | |
| 35 | Cut a trapezoid (upper base 4 cm, lower base 8 cm, height 5 cm) out of a rectangle (15×10 cm). Remaining area = ? | 🌳 | |
| 36 | A small cuboid (4×3×2 cm) is dug out of a large cuboid (10×8×6 cm). Remaining volume = ? | 🌳 | |
| 37 | A square has a side of 10 cm and is cut diagonally into two triangles. Area of each triangle = ? | 🌿 | |
| 38 | Two identical trapezoids (upper base 3 cm, lower base 7 cm, height 4 cm) are assembled into a hexagon "bottom to bottom". Total area = ? | 🌳 | |
| 39 | A rectangular park 50 m × 30 m. There is a straight path 2 m wide in the middle that runs through the long sides. Usable grass area = ? | 🏔️ | |
| 40 | The cube has a side length of 6 cm. The surface is painted and then cut into 27 small cubes with a side length of 2 cm. How many small cubes are there with "paint on one side"? | 🏔️ |
III. Geometry Ultimate Sprint (question 41-45 · 🚀 champion level challenge)
| # | Question | Difficulty | Working Space |
|---|---|---|---|
| 41 | A hexagon can be divided into a rectangle (8×6 cm) and two identical triangles (each base 4 cm and height 6 cm). Area of hexagon = ? | 🌳 | |
| 42 | If the side length of a cube is doubled, how many times its volume will increase? How many times does the surface area change? | 🏔️ | |
| 43 | Rectangle Parallelogram | 🏔️ | |
| 44 | A combined solid: a cuboid (20×10×8 cm) below and a cube (side length 4 cm) above in the center. Total volume = ? Surface area = ? (Note: The joint surface does not count as surface area) | 🏔️ | |
| 45 | Draw an irregular shape on graph paper (1 cm² per square). There are 24 complete squares, and about 8 half squares and most half squares. Estimated area = ? Write out your estimation method. | 🏔️ |
IV.areaformula cheat sheet
| graphics | areaformula | mostCommon Mistake |
|---|---|---|
| square | side length × side length | confused with perimeter |
| rectangle | length × width | confused with perimeter |
| parallelogram | Bottom ×high | Use hypotenuse as height |
| triangle | bottom × height÷ 2 | forget ÷2 |
| trapezoid | (upper bottom + lower bottom) × height ÷ 2 | Add height / forget ÷2 |
V. The Lessoncorecommon errorsummary
🎯 Review of Learning Objectives - After completing this lesson you should be able to:
☐ Identify all trap types in our hall
☐ Solve 🌱basic questions independently (100% correct)
☐ Challenge🌿Advanced questions (80%+ correct)
☐ Explain the lesson formula to classmates
| # | common error | trap | Correct Approach |
|---|---|---|---|
| 1 | Forget the area of a triangle ÷2 | T4 | Remember: base × height is a parallelogram, and a triangle only needs half |
| 2 | Parallelogram uses hypotenuse | T4 | The height must be the vertical distance, and the hypotenuse must be the interference item |
| 3 | Add height to the trapezoidal formula | T4 | The formula is (upper + lower) × height ÷ 2, not (upper + lower + height) × 2 |
| 4 | Area vs perimeter confusion | T4 | Perimeter = sum of side lengths (cm), area = calculated by formula (cm²) |
| 5 | Volume vs surface area confusion | T5 | Volume = cm³ (space occupied), surface area = cm² (sum of six side areas) |
| 6 | Capacity conversion error | T5 | 1 cm³ = 1 mL, 1000 cm³ = 1 L, must ÷1000 |
| 7 | Combined graphics overlap and repeat calculations | T4/T5 | After segmentation, check whether there is overlap. If there is overlap, you must subtract it once. |
| 8 | Area/volume unit spelled incorrectly | T4/T5 | The area must be written in cm²/m² and the volume must be written in cm³/m³ |
| 9 | Hidden dimensions are not calculated | T4/T5 | Some dimensions are not given directly and need to be inferred from other known dimensions. |
Strategies for getting perfect marks on geometry questions in sub-tests 🔴 Must read
Three-step verification method for geometry questions:
① Formula check |||SEP|||: Write the formula → Substitute the numbers → Confirm ÷2 / Not ÷2Unit check
② : Area → cm²/m², volume → cm³/m³, length → cm/mReasonability check
③ : For example, the area of a triangle < the area of a parallelogram with the same base and the same height? Is the area of the trapezoid reasonable?: For example, the area of a triangle < the area of a parallelogram with the same base and the same height? Is the area of the trapezoid reasonable?
① Formula check |||SEP|||: Write the formula → Substitute the numbers → Confirm ÷2 / Not ÷2Unit check
② : Area → cm²/m², volume → cm³/m³, length → cm/mReasonability check
③ : For example, the area of a triangle < the area of a parallelogram with the same base and the same height? Is the area of the trapezoid reasonable?: For example, the area of a triangle < the area of a parallelogram with the same base and the same height? Is the area of the trapezoid reasonable?
🧠 Tips for perfect score in geometry: "Recite formulas for area, divide triangles by two, use height instead of slant for squares, volume is cubic, and units must be understood clearly."
Lam Fung Academy · LF Academy · We don't teach math. We teach trap avoidance.