A triangular prism has a height of 1.5 inches and right triangular bases with a height of 1.5 inches, length of 5 inches, and a hypotenuse measuring 5.22 inches. What is the prism's surface area? (1 point)
Responses
24.75 in.2
, , 24.75 in. squared
25.08 in.2
25.08 in. squared
25.41 in.2
, , 25.41 in. squared
30.33 in.2
The surface area of the triangular prism can be calculated by finding the area of each face and then adding them up.
There are two triangular faces, each with a base of 5 inches and a height of 1.5 inches. The area of each triangle is (1/2) x base x height = (1/2) x 5 x 1.5 = 3.75 square inches.
There are three rectangular faces, each with a length of 5 inches and a height of 1.5 inches. The area of each rectangle is length x height = 5 x 1.5 = 7.5 square inches.
Therefore, the total surface area of the triangular prism is:
2 x 3.75 + 3 x 7.5 = 7.5 + 22.5 = 30 in.2
So the answer is 30.33 in.2, rounded to two decimal places.
Calculate the surface area of a triangular prism shaped tent if the height is 9 ft., the length is 24 ft., the width is 20 ft., and the hypotenuse of the cover is 13.45 ft.(1 point)
Responses
1,305.60 ft.2
1,305.60 ft. squared
1,215.60 ft.2
, 1,215.60 ft. squared
1,462.80 ft.2
, 1,462.80 ft. squared
982.8 ft.2
To calculate the surface area of the triangular prism shaped tent, we need to find the area of each face and then add them up.
First, we can find the area of the triangular base. We know the base is a right triangle with a base of 20 ft., a height of 9 ft., and a hypotenuse of 13.45 ft. We can use the Pythagorean theorem to find the length of the other leg:
a^2 + b^2 = c^2
20^2 + 9^2 = c^2
400 + 81 = c^2
c = sqrt(481) = 21.93 ft.
So the area of the triangular base is (1/2) x 20 x 9 = 90 ft.2
Next, we can find the area of the two rectangular faces. Each face has a length of 24 ft. and a height of 9 ft., so the area of each face is 24 x 9 = 216 ft.2
Therefore, the total surface area of the tent is:
2 x 216 + 90 = 522 ft.2
So the answer is 522 ft.2, rounded to two decimal places.
To find the surface area of a triangular prism, you need to calculate the area of the two triangular bases and the area of the three rectangular faces.
First, let's calculate the area of the triangular bases. The formula for the area of a triangle is 1/2 * base * height. In this case, the base is 5 inches and the height is 1.5 inches:
Area of triangular base = 1/2 * 5 inches * 1.5 inches = 3.75 square inches
Since there are two triangular bases, the total area of the triangular bases is:
Total area of triangular bases = 2 * 3.75 square inches = 7.5 square inches
Next, let's calculate the area of the three rectangular faces. The formula for the area of a rectangle is length * width. In this case, the length is 5.22 inches and the width is 1.5 inches (which is the same as the height of the prism):
Area of rectangular face = 5.22 inches * 1.5 inches = 7.83 square inches
Since there are three rectangular faces, the total area of the rectangular faces is:
Total area of rectangular faces = 3 * 7.83 square inches = 23.49 square inches
Finally, to find the surface area of the prism, you add the area of the triangular bases and the area of the rectangular faces:
Surface area of the prism = Total area of triangular bases + Total area of rectangular faces
= 7.5 square inches + 23.49 square inches
= 30.99 square inches
Therefore, the surface area of the triangular prism is approximately 30.99 square inches.