Question

A composite shape is drawn using a rectangle and a triangle. The rectangle has a base labeled as 6 centimeters. A triangle showing a perpendicular height of 6 centimeters is stacked on the top side of the rectangle. The base of the triangle and the top of the rectangle have a common side. Right angle symbols are shown on all four corners of the rectangle.

The area of the drawing is 78 square centimeters. What is the height of the rectangle?

Answer 1

Let the height of the rectangle be h centimeters.

The area of the rectangle is given by: 6h

The area of the triangle is given by: 1/2 * base * height = 1/2 * 6 * 6 = 18

Therefore, the total area of the composite shape is: 6h + 18 = 78

6h + 18 = 78
6h = 60
h = 10

Therefore, the height of the rectangle is 10 centimeters.