Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a right triangular prism placed on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 feet and a height of 8 feet. The width of the rectangular prism is 8 feet. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
What is the surface area of the figure?
(1 point)
To find the surface area of the figure, we need to calculate the surface area of each individual prism and then add them together.
The surface area of a rectangular prism is given by the formula: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
For the rectangular prism:
Surface area = 2(12)(8) + 2(12)(8) + 2(8)(8) = 192 + 192 + 128 = 512 square feet
The surface area of a right triangular prism can be calculated as the sum of the lateral area of the two triangular faces and the areas of the three rectangular faces.
For the right triangular prism:
The lateral area of the triangular faces = 2(1/2)(base)(height) = 2(1/2)(8)(15) = 120 square feet
The areas of the three rectangular faces = 2(8)(15) + 2(8)(8) + 2(15)(1) = 240 square feet
Therefore, the total surface area of the figure is:
512 + 120 + 240 = 872 square feet
So, the surface area of the figure is 872 square feet.