2023 · Q56
ABC is a triangle with sides AB = 41 cm, BC = 28 cm and CA = 15 cm. If D, E and F are the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF?
Elementary MathematicsMensuration
- A63 square cm
- B45 square cm
- C31.5 square cm
- D22.5 square cm
Explanation
D, E, F are midpoints, so △DEF is the medial triangle, whose area is exactly one-fourth of △ABC. For sides 41, 28, 15 the semiperimeter is s = 42, and Heron's formula gives area = √(42·1·14·27) = √(4·63²) = 126 cm². A quarter of this is 31.5 cm². The answer is (C).