Mathematics
Intermediate Mathematical Challenge
2023
4

4

The diagram shows a square, its two diagonals and two line segments, each of which connects two midpoints of sides of the square.

What fraction of the area of the square is shaded?

A. 1/8

B. 1/10

C. 1/12

D. 1/16

E. 1/24

Answer

D. 1/16

SOLUTIOn

The diagram shows that a triangle whose area is one quarter of that of the square may be divided into four congruent triangles, one of which is the shaded triangle.

So the required fraction is 1/4 × 1/4 = 1/16.

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