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
13 centimeters
13 centimeters
12 centimeters
12 centimeters
10 centimeters
10 centimeters
8 centimeters
8 centimeters
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page 16 of 16
To find the height of the rectangle, we need to determine the area of the rectangle and the area of the triangle, and then subtract the area of the triangle from the total area of the drawing.
The area of the rectangle is given by length * width. In this case, the width is 6 cm.
The area of the triangle is given by base * height / 2. In this case, the base of the triangle is also 6 cm.
The total area of the drawing is 78 square centimeters.
So, we have: length * 6 cm + 6 cm * 6 cm / 2 = 78 cm^2
Simplifying the equation:
length * 6 + 18 = 78
length * 6 = 60
length = 60 / 6
length = 10 cm
Therefore, the height of the rectangle is 10 centimeters.