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
8 centimeters
8 centimeters
13 centimeters
13 centimeters
10 centimeters
10 centimeters
12 centimeters
12 centimeters
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To find the height of the rectangle, we can use the formula for the area of a composite shape, which is area of rectangle + area of triangle.
The area of the rectangle is base * height, which is 6 * height = 6h.
The area of the triangle is 1/2 * base * height, which is 1/2 * 6 * 6 = 18.
So, the equation becomes 6h + 18 = 78.
Simplifying, we have 6h = 60.
Dividing both sides by 6, we get h = 10.
Therefore, the height of the rectangle is 10 centimeters.