Question
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?
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 calculated using the formula: 2lw + 2lh + 2wh, where l = length, w = width, and h = height.
For the rectangular prism:
Surface area = 2(12*8) + 2(12*8) + 2(8*8)
Surface area = 192 + 192 + 128
Surface area = 512 square feet
The surface area of a right triangular prism can be calculated by adding the area of the two triangular faces to the lateral area (area of the three rectangular faces) together.
To find the areas of the triangular faces:
Area = 0.5 * base * height
Area = 0.5 * 8 * 15
Area = 60 square feet
Since there are two triangular faces, the total area of the triangular faces is 120 square feet.
Now, to find the lateral area of the right triangular prism:
Lateral area = perimeter of base * height
Perimeter of base = sum of all edges of the base = 8 + 15 + 17 = 40 (since the hypotenuse is 17 using Pythagorean theorem)
Lateral area = 40 * h (where h is the height of the right triangular prism)
However, we do not know the height of the right triangular prism, so we cannot calculate the total surface area of the figure accurately without this information.