Question

The triangle inscribed within square abcd has, as its base, side ad, and has a height of 6 cm. if the area of the triangle is 21 cm2, what is the area of the shaded region?

Answer 1

Draw the diagram shown below to illustrate the problem.

Let x = length of a side of the enclosing square.

The area of the triangle is 21 cm², therefore
(1/2)*x*6 = 21
3x = 21
x = 7 cm

The area of the square is
7*7 = 49 cm²

The area of the shaded region is
49 - 21 = 28 cm²

Answer: 28 cm²