The bases of a prism are right trinanges with side lengths 6 meters, 8 meters and 10.. The height of the prism is 3 meters. What's is the lateral area of the prism? What is the total surface area?
do it this way:
both ends= 2*6*8
side one: 6*3
side two: 8*3
side three: 10*3
add them.
To find the lateral area of the prism, we need to calculate the sum of the areas of the four lateral faces. Since the bases of the prism are right triangles with side lengths 6 meters, 8 meters, and 10 meters, we can use the formula for the area of a right triangle, which is 1/2 times the product of the two legs.
The height of the prism is given as 3 meters, which is the same as the altitude of the right triangles. So, the lateral area of each triangular face is given by 1/2 times the product of the two legs, namely 1/2 times 6 times 8, which equals 24 square meters. Since there are four triangular faces, the total lateral area is 4 times 24, which equals 96 square meters.
To calculate the total surface area of the prism, we need to consider the area of the two triangular bases in addition to the four lateral faces. The area of each triangular base can be found by using the formula for the area of a right triangle, which is 1/2 times the product of the two legs, namely 1/2 times 6 times 8, which equals 24 square meters. Since there are two bases, the total area of the bases is 2 times 24, which equals 48 square meters.
Adding the lateral area (96 square meters) and the area of the bases (48 square meters), we get the total surface area of the prism, which is 96 + 48 = 144 square meters. Hence, the lateral area of the prism is 96 square meters, and the total surface area is 144 square meters.