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CAT 2021 Slot 2 · Quant · Polygons and Quadrilaterals · medium

E is the midpoint of BC and F is the midpoint of CD. What is the area (in cm²) of triangle AEF?

Single correct option

ABCD is a square of side 10 cm. E is the midpoint of BC and F is the midpoint of CD. What is the area (in cm²) of triangle AEF?
  1. A. 32.5
  2. B. 35
  3. C. 37.5
  4. D. 40
Show answer and solution

Answer: (C) 37.5

Subtract the three corner triangles from the square.

- Triangle ABE: ½ × 10 × 5 = 25
- Triangle ECF: ½ × 5 × 5 = 12.5
- Triangle ADF: ½ × 10 × 5 = 25

Area of AEF = 100 − (25 + 12.5 + 25) = 37.5 cm².

Check with coordinates: A(0,0), E(10,5), F(5,10): area = ½|10·10 − 5·5| = ½ × 75 = 37.5 ✓.
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Original question written in the CAT 2021 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake