What is the lateral area of a rectangular pentagon pyramid that has a slant height of 16 in. and a base side length of 8 in.
A rectangular pentagon pyramid has 5 rectangular lateral faces and a pentagonal base.
Each lateral face has a length of 8 in and a height of 16 in, since the slant height is the height of each triangular face.
Therefore, the lateral area of one face is:
lateral area of one face = 8 in x 16 in/2 = 64 in^2
Since there are 5 lateral faces, the total lateral area is:
total lateral area = 5 x 64 in^2 = 320 in^2
Answer: 320 square inches
To find the lateral area of a rectangular pentagonal pyramid, we need to find the area of each face and then add them up.
Step 1: Find the area of the base
The base of the pyramid is a rectangular pentagon, which means it has five sides. Since it's a rectangle, we can calculate its area by multiplying the length and the width.
Given that the base side length is 8 inches, the width and length of the base are both 8 inches.
Therefore, the area of the base is: 8 inches x 8 inches = 64 square inches.
Step 2: Find the area of each triangular face
The pyramid has five triangular faces. To find the area of a triangle, we need the base and the height. The base of each triangular face is the same as the base of the pyramid (8 inches). The height of each triangular face is the slant height of the pyramid (16 inches).
To find the area of each triangular face, we can use the formula for the area of a triangle: A = (1/2) x base x height.
Given that the base is 8 inches and the height is 16 inches, the area of each triangular face is: (1/2) x 8 inches x 16 inches = 64 square inches.
Step 3: Calculate the total lateral area
Since the pyramid has five triangular faces, we need to calculate the total area of the five triangular faces and add it to the area of the base.
Total lateral area = (Area of the base) + (Area of each triangular face x 5)
Total lateral area = 64 square inches + (64 square inches x 5)
Total lateral area = 64 square inches + 320 square inches
Total lateral area = 384 square inches
Therefore, the lateral area of the rectangular pentagonal pyramid is 384 square inches.