Triangle ABC is a right triangle with legs 4 cm and 5 cm. Triangle DEF is similar to ABC and the ratio of their corresponding sides is 1:4. What is the area of triangle DEF?

hard 4 marks Class 6 · Mathematics · Understanding Elementary Shapes

Answer

160 cm²

The correct answer is 160 cm² — Since triangles are similar, areas scale as the square of side ratio: $(\frac{1}{4})^{2} = \frac{1}{16}$ for ABC to DEF. Thus area of DEF = $10 \times 16 = 160$ cm².

Step-by-step solution

Compute area of triangle ABC: $\frac{1}{2} \times 4 \times 5 = 10$ cm².
Since triangles are similar, areas scale as the square of side ratio: $(\frac{1}{4})^{2} = \frac{1}{16}$ for ABC to DEF. Thus area of DEF = $10 \times 16 = 160$ cm².

Common mistake: Using linear ratio instead of squared ratio

Concept tested: Area scaling in similar triangles

Published 13 October 2026 · How this solution was prepared and checked

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