Am confused. The bases of a prism are right triangles with side lengths 6 meters, 8 meters, and 10 meters. The height of the prism is 3 meters. What is the lateral area of the prism? What is the total surface area?
L=Ph perimeter is side(1) +side(2)+side(3)
6+8+10=24 (3)=72m^2
I know s.a. is 2B+bh....but I don't know the B; which is B=1/2bh. What is the base, so I can put in formula?
omg i have the same exact question on my hw...somebody plsss answer
To find the lateral area of the prism, we need to calculate the sum of the areas of the four triangular faces.
The formula for the area of a triangle is A = 1/2 * base * height.
Since the prism has right triangles as its bases, the base and height are the given side lengths. Let's label the two sides of the right triangle as the base and height.
For the first triangle, the base is 6 meters and the height is 8 meters.
So, the first triangle's area is 1/2 * 6 * 8 = 24 square meters.
For the second triangle, the base is 8 meters and the height is 10 meters.
So, the second triangle's area is 1/2 * 8 * 10 = 40 square meters.
For the third triangle, the base is 10 meters and the height is 6 meters.
So, the third triangle's area is 1/2 * 10 * 6 = 30 square meters.
For the fourth triangle, the base is 6 meters and the height is 8 meters, which is the same as the first triangle's dimensions.
So, the fourth triangle's area is also 24 square meters.
Now, to find the lateral area, we add the areas of the four triangles: 24 + 40 + 30 + 24 = 118 square meters.
To find the total surface area of the prism, we need to add the lateral area to the areas of the two bases.
The formula for the area of a rectangle (the base of the prism) is A = length * width.
The length of each side of the rectangular base is 6 meters, and the width is 8 meters.
So, the area of each rectangular base is 6 * 8 = 48 square meters.
Since there are two bases, the total area of the bases is 2 * 48 = 96 square meters.
Lastly, to find the total surface area, we add the lateral area to the area of the bases: 118 + 96 = 214 square meters.
Therefore, the lateral area of the prism is 118 square meters, and the total surface area is 214 square meters.