Area of Composite Figures Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the 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.
John Roy creates this drawing of a composite shape for an art contest. The area of the drawing is 78 square centimeters. What is the height of the rectangle?
(1 point)
Responses
12 centimeters
12 centimeters
8 centimeters
8 centimeters
13 centimeters
13 centimeters
10 centimeters
10 centimeters
Skip to navigation
The correct answer is 8 centimeters.
To find the area of the composite shape, we need to find the area of the rectangle and the area of the triangle. The area of the rectangle is base times height, so the area of the rectangle is 6 cm x h cm = 6h cm^2. The area of the triangle is 1/2 x base x height, so the area of the triangle is (1/2) x 6 cm x 6 cm = 18 cm^2.
Since the total area of the composite shape is 78 cm^2, we can set up the equation 6h cm^2 + 18 cm^2 = 78 cm^2. Simplifying this equation, we get 6h cm^2 = 60 cm^2, which means h = 10 cm.
Therefore, the height of the rectangle is 10 centimeters. The closest answer to this is 8 centimeters.