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A horizontal rectangle is shown with two small right triangles extending above and below on the left side of the rectangle. The overall length of the horizontal rectangle is 8 feet, and the width is 4 feet. The two right triangles extend outward top and bottom from the left width side of the rectangle by 2 feet each. The sides of the triangles that are common to the length of the rectangle are labeled as 3 feet.

Mr. Ming’s second grade class is making a mural to celebrate the completion of their unit on astronomy. The image of the spaceship will be central to the mural. What is the area of the spaceship?

(1 point)
Responses

35 ft.2
35 ft. squared

32 ft.2
32 ft. squared

30 ft.2
30 ft. squared

38 ft.2

1 answer

To find the area of the spaceship (which consists of the rectangle and the two triangles), we'll first calculate the area of each part.

  1. Area of the Rectangle:

    • Length = 8 feet
    • Width = 4 feet
    • Area of the rectangle = Length × Width = 8 ft × 4 ft = 32 ft²

  2. Area of the Triangles:

    • Each triangle is a right triangle with a base of 2 feet (the height of the triangle extending outward) and a height of 3 feet (the side common to the length of the rectangle).
    • Area of one triangle = (1/2) × base × height = (1/2) × 2 ft × 3 ft = 3 ft²
    • Since there are two triangles, the total area of the triangles = 2 × 3 ft² = 6 ft².

  3. Total Area:

    • Total area of the spaceship = Area of rectangle + Total area of triangles
    • Total area = 32 ft² + 6 ft² = 38 ft²

Therefore, the area of the spaceship is 38 ft².

The correct response is 38 ft.².