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)
• 12 centimeters
• 13 centimeters
• 10 centimeters
• 8 centimeters
To find the height of the rectangle, we need to determine the dimensions of the rectangle.
Let's call the height of the rectangle 'h' and the width 'w'. Since the drawing is a composite shape, it consists of a rectangle and a triangle.
The area of the rectangle is: width * height = w * h
The area of the triangle is: 1/2 * base * height = 1/2 * w * h
Given that the total area of the composite shape is 78 square centimeters:
w * h + 1/2 * w * h = 78
w * h + 0.5 * w * h = 78
1.5 * w * h = 78
w * h = 78 / 1.5
w * h = 52
Since we know the area of the rectangle (52 square centimeters), and we need to find the height of the rectangle, we can try different combinations of values for width and height until we find the correct one.
Let's try the options:
1. h = 12, w = 4
12 * 4 = 48 (rectangle area)
1/2 * 4 * 12 = 24 (triangle area)
48 + 24 = 72
2. h = 13, w = 4
13 * 4 = 52 (rectangle area)
1/2 * 4 * 13 = 26 (triangle area)
52 + 26 = 78
Therefore, the height of the rectangle is 13 centimeters.