The ratio of areas of similar figures
Answers are for parents and teachers.
1
Two similar triangles have areas 18 cm² and 50 cm². The perimeter of the larger is 60 cm. Find the perimeter of the smaller.
18 : 50 = 9 : 25, so k = 3 : 5. The perimeter of the smaller is 60 × 3/5 = 36 cm.
2
DE ∥ BC with AD = 4 and DB = 6. The area of △ADE is 48 m². Find the area of △ABC and of the trapezium DBCE.
AB = 10, k = 4/10 = 2/5, area(ABC) = 48 ÷ 4/25 = 300 m². Trapezium = 300 − 48 = 252 m².
3
Two similar polygons have corresponding sides 5 m and 8 m. The smaller has area 100 m². Find the larger area.
k² = 64/25, so the area is 100 × 64/25 = 256 m².
4
A model of a school at the scale 1 : 50 has a floor of 0.4 m². Find the real floor area.
0.4 × 50² = 0.4 × 2500 = 1000 m².
5
Painting a triangular wall panel of area 6 m² costs 120 LE. A similar panel has every side 3 times as long. How much does it cost to paint at the same price per m²?
The price is 20 LE per m². The new area is 6 × 3² = 54 m², so the cost is 54 × 20 = 1080 LE (9 times, not 3 times).