Question

In the given figure, ABCD is a square and E, F, G, H are the mid-points of its sides. If the length of AB is 4 cm, what will be the area of the square EFGH?

• A. 8 cm${}^2$
• B. 16 cm${}^2$
• C. 12 cm${}^2$
• D. 4 cm${}^2$

Answer 1

The correct option is A 8 cm${}^2$

In the given figure, if we join EG and HF, square ABCD will break down the figure into 8 triangles, which will all have the same area.

Since four triangles are in the square EFGH, we can say that area of EFGH is half of the area of sqaure ABCD.


Area of ABCD = $4\times 4$ = $16$ cm${}^2$
Area of square EFGH = $\frac{1}{2}\times 16$ = $8$ cm${}^2$