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
10 centimeters
10 centimeters
13 centimeters
13 centimeters
8 centimeters
8 centimeters
12 centimeters
12 centimeters
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The correct answer is 12 centimeters.
To find the area of the composite shape, we need to find the area of the rectangle and the area of the triangle separately.
Area of Rectangle = base x height = 6 cm x h = 6h square centimeters
Area of Triangle = 1/2 x base x height = 1/2 x 6cm x 6cm = 18 square centimeters
Total Area = 6h + 18
78 = 6h + 18
6h = 60
h = 10
Since the height of the triangle is given as 6 cm, the height of the rectangle would be 10 cm - 6 cm = 4 cm.
Therefore, the height of the rectangle is 12 centimeters.