Geometry and proof · Ages 14–15

Areas of similar figures worksheet

Part of: Similar triangles

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Geometry and proof · Ages 14–15

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.

1.Two similar figures have sides in the ratio 4 : 7, so their areas are in the ratio 16 :
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2.Two similar triangles have corresponding sides in the ratio 1 : 5. The big triangle's area is times the small one's.
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3.Two similar triangles have corresponding sides in the ratio 1 : 9. The big triangle's area is times the small one's.
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4.Two similar figures have sides in the ratio 3 : 4, so their areas are in the ratio 9 :
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5.△ABC ~ △PQR, with AB = 4 cm and PQ = 5 cm. The area of △ABC is 32 cm². The area of △PQR =
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6.In the picture, DE // BC, and the area of △ADE is 48 cm². The area of △ABC =
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7.Two similar triangles have areas 48 cm² and 75 cm². A side of the small one is 4 cm; the matching side of the big one =
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8.In the picture, DE // BC, and the area of △ADE is 64 cm². The area of △ABC = cm², and of DBCE = cm².
Fill in each blank
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9.Two similar triangles have areas 8 cm² and 18 cm². A side of the small one is 8 cm; the matching side of the big one =
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10.In the picture, DE // BC, and the area of △ADE is 9 cm². The area of △ABC = cm², and of DBCE = cm².
Fill in each blank
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13.Two triangular lawns have the same shape, their sides in the ratio 2 : 5. The small lawn is 24 m². The big lawn is m²; a bag of seed covers 5 m², so it needs bags.
Fill in each blank
Working:
Answer:
14.A map's scale is 1 : 500. A plot of land covers 7 cm² on the map. 1 cm on the map stands for m, 1 cm² for m², so the plot is really m².
Fill in each blank
Working:
Answer:
15.The ink to print a photo costs in proportion to its area. A small photo costs $8. Enlarged in proportion, each side 4 times as long, what does it cost?
Working:
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16.Two similar triangular tiles have areas of 9 cm² and 49 cm². In lowest terms, their areas are in the ratio : , and their sides in the ratio : .
Fill in each blank
Working:
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17.Two similar triangular tiles have areas of 125 cm² and 180 cm². In lowest terms, their areas are in the ratio : , and their sides in the ratio : .
Fill in each blank
Working:
Answer:
18.A map's scale is 1 : 2000. A plot of land covers 12 cm² on the map. 1 cm on the map stands for m, 1 cm² for m², so the plot is really m².
Fill in each blank
Working:
Answer:

Show the answers and working

Areas of similar figures worksheet: Answers and working

1. 49
Area ratio = 4² : 7² = 16 : 49.
2. 25
The area ratio is the side ratio squared: 5² = 25.
3. 81
The area ratio is the side ratio squared: 9² = 81.
4. 16
Area ratio = 3² : 4² = 9 : 16.
5. 50 cm²
Areas are 4² : 5²: 32 × 5² ÷ 4² = 50 cm².
6. 147 cm²
△ADE ~ △ABC with sides AD : AB = 4 : 7, so areas 4² : 7²: 48 × 7² ÷ 4² = 147 cm².
7. 5 cm
Areas 48 : 75 = 4² : 5²; the square root gives sides 4 : 5: 4 × 5 ÷ 4 = 5 cm.
8. 324, 260
Areas 4² : 9²: △ABC = 324 cm²; DBCE = 324 − 64 = 260 cm².
9. 12 cm
Areas 8 : 18 = 2² : 3²; the square root gives sides 2 : 3: 8 × 3 ÷ 2 = 12 cm.
10. 49, 40
Areas 3² : 7²: △ABC = 49 cm²; DBCE = 49 − 9 = 40 cm².

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 150, 30
Areas 2² : 5²: 24 × 5² ÷ 2² = 150 m²; 150 ÷ 5 = 30 bags.
14. 5, 25, 175
1 cm stands for 500 cm = 5 m; areas square it: 1 cm² stands for 5 × 5 = 25 m²; 7 × 25 = 175 m².
15. 128 dollars
Each side times 4, so the area times 4² = 4 × 4: 8 × 4 × 4 = 128 dollars.
16. 9, 49, 3, 7
9 : 49 = 3² : 7²; the square root gives sides 3 : 7.
17. 25, 36, 5, 6
125 : 180 = 5² : 6²; the square root gives sides 5 : 6.
18. 20, 400, 4800
1 cm stands for 2000 cm = 20 m; areas square it: 1 cm² stands for 20 × 20 = 400 m²; 12 × 400 = 4800 m².

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