Find the surface area of this triangular prism 24 in 25 in 14 in 32 in and 25 in
Ion even wanna read all that Vro. I believe jiskha is used for answers not life stories
Camden that didnāt help at allš¤
yo can I get the answer?
To find the surface area of a triangular prism, we need to find the areas of all the individual faces and then sum them up.
A triangular prism has two triangular faces and three rectangular faces.
For the triangular faces:
1. To find the area of the first triangular face, we need the length of the base and the height of the triangle. In this case, the base is 24 inches and the height is 25 inches. The formula to find the area of a triangle is A = (1/2) * base * height. Substituting the values, we have A1 = (1/2) * 24 in * 25 in.
2. The second triangular face has the same dimensions as the first one, so its area is also A2 = (1/2) * 24 in * 25 in.
For the rectangular faces:
1. To find the area of the first rectangular face, we need the length and width of the rectangle. One side of the rectangle is the height of the prism, which is 14 inches. The other side is the length of the prism, which is 24 inches. The formula to find the area of a rectangle is A = length * width. Substituting the values, we have A3 = 24 in * 14 in.
2. The second rectangular face has the same dimensions as the first one, so its area is also A4 = 24 in * 14 in.
3. The third rectangular face is the base of the prism, which is a rectangle with length 32 inches and width 25 inches. So, its area is A5 = 32 in * 25 in.
Now, we can sum up all the areas to get the total surface area of the prism:
Total surface area = A1 + A2 + A3 + A4 + A5
Substituting the values we calculated:
Total surface area = (1/2) * 24 in * 25 in + (1/2) * 24 in * 25 in + 24 in * 14 in + 24 in * 14 in + 32 in * 25 in
Simplifying:
Total surface area = 300 inĀ² + 300 inĀ² + 336 inĀ² + 336 inĀ² + 800 inĀ²
Finally, adding all the values:
Total surface area = 2072 inĀ²
Therefore, the surface area of the given triangular prism is 2072 square inches.
SA=bh+(s1+s2+s3)H
b = base; h = height of the triangle; s1, s2, and s3 = the length of each side of the triangle base, and H = the height of the prism (which is the length of the of the rectangles)
Hope this helped! If you need further explanation of the formula or help guiding you through a problem just reply and I will for sure help!