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?

Question

(1 point)
Responses

10 centimeters
10 centimeters

13 centimeters
13 centimeters

8 centimeters
8 centimeters

12 centimeters

This image shows a vertical rectangle. Its base is 6 cm. On the top of the rectangle there is a triangle. The triangle’s hight is 6 cm.

Answer 1

To solve for the height of the rectangle, we can use the information provided about the area of the composite shape, which consists of the rectangle and the triangle on top of it.

1. Calculate the area of the triangle:

   • The area of a triangle is given by the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
   • The base of the triangle is the same as the base of the rectangle, which is 6 cm, and the height of the triangle is given as 6 cm.
   • Plugging in these values: \[ \text{Area of triangle} = \frac{1}{2} \times 6 \times 6 = \frac{36}{2} = 18 \text{ square centimeters} \]

2. Determine the area of the rectangle:

   • The total area of the composite shape is given as 78 square centimeters.
   • We can find the area of the rectangle by subtracting the area of the triangle from the total area: \[ \text{Area of rectangle} = \text{Total area} - \text{Area of triangle} = 78 - 18 = 60 \text{ square centimeters} \]

3. Find the height of the rectangle:

   • The area of a rectangle is given by: \[ \text{Area} = \text{base} \times \text{height} \]
   • Using the known area and base (6 cm), we can find the height: \[ 60 = 6 \times \text{height} \] \[ \text{height} = \frac{60}{6} = 10 \text{ centimeters} \]

Thus, the height of the rectangle is 10 centimeters.