Perimeter, area and volume · Ages 10–11
Areas of polygons worksheet
Part of: Areas of parallelograms, triangles and trapeziums
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Areas of polygons worksheet
Perimeter, area and volume · Ages 10–11
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.What is the area of the polygon in the picture?
Answer:
2.What is the area of the polygon in the picture?
Answer:
3.What is the area of the polygon in the picture?
Answer:
4.What is the area of the polygon in the picture?
Answer:
Part B: Choose, or true or false (2 marks each)
5.Which working finds the area of the polygon in the picture?
- A. 18 × 12
- B. 18 × 8 + 13 × 12
- C. 18 × 12 − 13 × 8
- D. 18 × 12 − 5 × 4
Choose the right answer
Answer:
6.The polygon in the picture has an area of 132 cm².
True or false?
Answer:
7.The polygon in the picture has an area of 144 cm².
True or false?
Answer:
8.The polygon in the picture has an area of 84 cm².
True or false?
Answer:
9.The polygon in the picture has an area of 112 cm².
True or false?
Answer:
10.The polygon in the picture has an area of 120 cm².
True or false?
Answer:
11.The polygon in the picture has an area of 117 cm².
True or false?
Answer:
12.The polygon in the picture has an area of 180 cm².
True or false?
Answer:
Part C: Word problems (4 marks each)
13.The picture is the plan of an L-shaped living room. Flooring costs $120 a square metre. How many dollars does flooring the whole room cost?
Working:
Answer:
14.Tsz-ching saws a corner off a rectangular board, leaving the piece in the picture. What is the area of what is left, in cm²?
Working:
Answer:
15.The picture is the plan of a U-shaped garden. What is its area in square metres?
Working:
Answer:
16.The picture shows a house-shaped wall. How many square metres of it are to be painted, all of it?
Working:
Answer:
17.The picture is the plan of an L-shaped living room. Flooring costs $80 a square metre. How many dollars does flooring the whole room cost?
Working:
Answer:
18.Ka-yee saws a corner off a rectangular board, leaving the piece in the picture. What is the area of what is left, in cm²?
Working:
Answer:
Show the answers and working
Areas of polygons worksheet: Answers and working
Part A: Working out and filling in
1. 145 cm²
Fill in the missing corner and it is a 11 × 15 rectangle. Then find how long and wide the corner is.
Fill it in to a 11 × 15 rectangle, then take off the corner (11 − 6) × (15 − 11): 145.
2. 154 cm²
Split the shape into a rectangle and a triangle; the triangle's base is 14 and its height 6.
Cut into a rectangle and a triangle: 14 × 8 + 14 × 6 ÷ 2 = 154.
3. 120 cm²
Fill in the notch to make a 16 × 8 rectangle. Work that out, then take off the 4 × 2 notch.
Fill in to a 16 × 8 rectangle and take off the 4 × 2 notch: 120.
4. 135 cm²
Fill it in to a 13 × 12 rectangle; what is missing is a right-angled triangle. How long are its two short sides?
Fill in to 13 × 12 and take off the right-angled triangle with legs 13 − 6 and 12 − 6: 135.
Part B: Choose, or true or false
5. D. 18 × 12 − 5 × 4
Fill it in to a 18 × 12 rectangle first. The missing corner is 18 − 13 long and 12 − 8 wide.
The corner is 18 − 13 = 5 by 12 − 8 = 4; the big rectangle less the corner: 18 × 12 − 5 × 4.
6. False
Split into the 11 × 8 rectangle and the 11 × 4 ÷ 2 triangle; find the total and compare it with 132.
Rectangle 11 × 8, plus triangle 11 × 4 ÷ 2 (a triangle is halved): 110.
7. False
Split into the 12 × 9 rectangle and the 12 × 3 ÷ 2 triangle; find the total and compare it with 144.
Rectangle 12 × 9, plus triangle 12 × 3 ÷ 2 (a triangle is halved): 126.
8. False
Split into the 12 × 4 rectangle and the 12 × 3 ÷ 2 triangle; find the total and compare it with 84.
Rectangle 12 × 4, plus triangle 12 × 3 ÷ 2 (a triangle is halved): 66.
9. True
Split into the 7 × 12 rectangle and the 7 × 8 ÷ 2 triangle; find the total and compare it with 112.
Rectangle 7 × 12, plus triangle 7 × 8 ÷ 2 (a triangle is halved): 112.
10. False
Split into the 15 × 6 rectangle and the 15 × 2 ÷ 2 triangle; find the total and compare it with 120.
Rectangle 15 × 6, plus triangle 15 × 2 ÷ 2 (a triangle is halved): 105.
11. False
Split into the 9 × 7 rectangle and the 9 × 6 ÷ 2 triangle; find the total and compare it with 117.
Rectangle 9 × 7, plus triangle 9 × 6 ÷ 2 (a triangle is halved): 90.
12. True
Split into the 12 × 12 rectangle and the 12 × 6 ÷ 2 triangle; find the total and compare it with 180.
Rectangle 12 × 12, plus triangle 12 × 6 ÷ 2 (a triangle is halved): 180.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 9360 dollars
Fill in the missing corner and the room is a 14 × 6 rectangle. Take off the corner for the area, then multiply by $120.
The missing corner is 14 − 12 = 2 m by 6 − 3 = 3 m. Area = 14 × 6 − 2 × 3 = 78 m², and 78 × 120 = $9,360.
14. 134 cm²
The board was a 9 × 16 rectangle, and the piece sawn off is a right-angled triangle. Use the sides in the picture to find its two short sides.
The whole board 9 × 16, less the right-angled triangle sawn off: 134 cm².
15. 168 m²
Fill in the middle notch to make a 16 × 11 rectangle, then take off the 2 × 4 notch.
The whole rectangle 16 × 11 less the middle notch 2 × 4: 168 m².
16. 55 m²
Split the wall into the rectangle below and the triangular top; the triangle's base is 11 and its height 4.
Rectangle 11 × 3 plus the triangular top 11 × 4 ÷ 2: 55 m².
17. 9120 dollars
Fill in the missing corner and the room is a 14 × 11 rectangle. Take off the corner for the area, then multiply by $80.
The missing corner is 14 − 9 = 5 m by 11 − 3 = 8 m. Area = 14 × 11 − 5 × 8 = 114 m², and 114 × 80 = $9,120.
18. 135 cm²
The board was a 17 × 10 rectangle, and the piece sawn off is a right-angled triangle. Use the sides in the picture to find its two short sides.
The whole board 17 × 10, less the right-angled triangle sawn off: 135 cm².
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