Note: Figure not drawn to scale.
Height has been rounded for computational ease.
If X = 7 units, Y = 6 units, Z = 16 units, and h = 6 units, what is the surface area of the triangular prism shown above?
(2 points)
Responses
288 square units
288 square units
392 square units
392 square units
372 square units
372 square units
356 square units
To find the surface area of the triangular prism, we first calculate the lateral surface area of the prism.
The lateral surface area can be found by adding the areas of the three rectangles that make up the sides of the prism.
The area of the first rectangle is:
Base (X) * height (h) = 7 * 6 = 42 square units
The area of the second rectangle is:
Base (Y) * height (h) = 6 * 6 = 36 square units
The area of the third rectangle is:
Base (Z) * height (h) = 16 * 6 = 96 square units
Now, we add up all three areas to find the lateral surface area:
42 + 36 + 96 = 174 square units
Next, we need to calculate the area of the two triangular bases.
The area of a triangle is given by: 1/2 * base * height.
The base of the triangle is the same as the width of the rectangular faces (Z), and the height of the triangle is given as X in this case.
So the area of each of the triangular bases is:
1/2 * 16 * 7 = 56 square units
Therefore, the total surface area of the triangular prism is:
Lateral surface area + 2 * area of triangular bases
= 174 + 2 * 56
= 174 + 112
= 286 square units
Therefore, the surface area of the triangular prism given the dimensions X = 7 units, Y = 6 units, Z = 16 units, and h = 6 units is 286 square units.
try again
Let's find the surface area of the triangular prism step by step.
1. Find the lateral surface area:
Lateral surface area = perimeter of the base * height
Perimeter of the base = X + Y + Z
Perimeter of the base = 7 + 6 + 16 = 29 units
Lateral surface area = 29 * h = 29 * 6 = 174 square units
2. Find the area of each triangular base:
Area = 0.5 * base * height
Area = 0.5 * Z * X = 0.5 * 16 * 7 = 56 square units
3. The total surface area of the triangular prism is:
Total surface area = Lateral surface area + 2 * Area of one base
Total surface area = 174 + 2 * 56 = 174 + 112 = 286 square units
Therefore, the surface area of the triangular prism is 286 square units.