To find the height of the rectangle, we need to determine the height of the triangle. The area of the composite shape can be calculated by the sum of the areas of the rectangle and the triangle.
Area of rectangle = base x height = 6 cm x height
Area of triangle = (1/2) x base x height = 0.5 x 6 cm x height = 3 cm x height
Therefore, the total area is 6 cm x height + 3 cm x height = 78 square centimeters
Simplifying, we get: 9 cm x height = 78 square centimeters
Therefore, height = 78 square centimeters / 9 cm = 8.67 cm
So, the height of the rectangle is approximately 8.67 centimeters.
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
8 centimeters
8 centimeters
10 centimeters
1 answer