The area of a triangle ABC is 16 cm². If a similar triangle DEF has sides that are twice the length of ΔABC’s sides, what is the…

Question

The area of a triangle ABC is 16 cm². If a similar triangle DEF has sides that are twice the length of ΔABC’s sides, what is the area of ΔDEF?

1. A. 32 cm²
2. B. 48 cm²
3. C. 64 cm² (Correct answer)
4. D. 80 cm²

Correct Answer

Option C — 64 cm²

Detailed Solution & Explanation

The correct answer is 64 cm².

Key Points

• For similar triangles, the ratio of areas equals the square of the ratio of corresponding sides.
• DEF's sides are twice ABC's, so the area ratio is 2² = 4.
• Area of DEF = 4 × 16 = 64 cm².
• Always square the linear scale factor for areas (and cube it for volumes) — doubling the sides quadruples the area, it does not merely double it.