Question

The diagram below shows a rectangle with side lengths 4 and 8 and a square with side length 5. Three vertices of the square lie on three different sides of the rectangle, as shown. What is the area of the region inside both the square and the rectangle?

Answer 1

The area of the region inside both the square and the rectangle is 37 square units.

Explanation:

The area of the region inside both the square and the rectangle can be found by subtracting the areas of the four triangles outside the square from the area of the rectangle.

The area of the rectangle is 4 * 8 = 32 square units. The area of each triangle can be found using the formula for the area of a triangle, which is (base * height) / 2. The base of each triangle is half the length of the side of the square, which is 5 / 2 = 2.5 units. The height of each triangle is the difference in height between the rectangle and the square, which is 4 - 5 = -1 unit. The area of each triangle is (2.5 * -1) / 2 = -1.25 square units. The area of the four triangles outside the square is 4 * -1.25 = -5 square units.

The area of the region inside both the square and the rectangle is 32 + 5 = 37 square units.