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?
To find the height of the rectangle, we first need to find the area of both the rectangle and the triangle separately.
Area of rectangle = length x width
Area of rectangle = 6 cm x h cm
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 6 cm x h cm
Total area = area of rectangle + area of triangle
78 cm^2 = (6 cm x h cm) + (1/2 x 6 cm x h cm)
78 cm^2 = 6h + 3h
78 cm^2 = 9h
h = 78 cm^2 / 9
h = 8.67 cm
Therefore, the height of the rectangle is approximately 8.67 centimeters.