Answer:
Surface area = 96 square units
Explanation:
The surface area of a rectangular prism is simply the sum of all the areas of the 2-D that make up the rectangular prism. In this prism, there are:
- two triangles with the same base and height,
- two rectangles with the same length and width,
- and one rectangle in the middle.
Thus, we can find the area of the individual shapes, and the sum of these areas is the surface area of the triangular units in square units:
Area of the triangles:
Because the two triangles have the same dimensions, we can find the area of one triangle and multiply it by two to find the total area of both triangles.
The formula for the area of a triangle is given by:
A = 1/2bh, where
- A is the area in square units,
- b is the base,
- and h in the height.
Since the base of both triangles is 6 units and the height is 2 units, we can plug in 6 for b and 2 for h to find A, the area of one triangle in square units:
A = 1/2(6)(2)
A = 3(2)
A = 6
Now we can multiply this area by 2 to find the total area of both triangles:
2A = 2(6)
2A = 12
Thus, the total area of both triangles is 12 square units:
Area of the left and right rectangles:
Similar to the triangles, the congruence of the two rectangles on the left and right allows us to find the area of one rectangle and later double it to find the total area of these two rectangles.
The formula for the area of a rectangle is given by:
A = lw, where
- A is the area in square units,
- l is the length,
- and w is the width.
Since the length of both rectangles (on the left and right) is 7 units and the width is 3 units, we can plug in 7 for l and 3 for w to find A, the area of one of the two rectangles (on the left and right):
A = 7 * 3
A = 21
Now we can double this area to find the total area of the two rectangles on the left and right:
2A = 2(21)
2A = 42
Thus, the total area of the two rectangles (on the left and right) is 42 square units:
Area of the middle rectangle:
Now we can find the area of the middle rectangle by first identifying the length and width and then by plugging into the rectangle area formula. Since the length is 7 units and the width is 6 units, we can plug in 7 for l and 6 for w to find A, the area of the middle rectangle in square units:
A = 7 * 6
A = 42
Thus, the area of the middle rectangle is 42 square units:
Surface area of the triangular prism:
Since we now know the area of all five shapes that compose the triangular prism, finding the sum of these areas will give us SA, the surface area of the triangular prism in square units:
SA = 12 + 42 + 42
SA = 54 + 42
SA = 96
Thus, the surface area of the triangular prism is 96 square units.