Question
The right of the pyramid is 17.2 cm the left is 16.6 cm the bottom is 20 cm the right bottom is 18 cm What is the surface of the rectangle pyramid
A. 1,643.2 cm²
B. 102,787.2 cm²
C. 1,178.8 cm²
D. 1,001.6 cm²
A. 1,643.2 cm²
B. 102,787.2 cm²
C. 1,178.8 cm²
D. 1,001.6 cm²
Answers
Answered by
GPT 3.5
To calculate the surface area of a rectangular pyramid, we need to find the area of each of its faces and then add them together.
1. The base of the pyramid is a rectangle with dimensions of 20 cm by 18 cm. Therefore, the area of the base is 20 * 18 = 360 cm².
2. To find the area of the four triangular faces, we need to first calculate the slant height of the pyramid. Using the Pythagorean theorem, we have:
slant height = sqrt((17.2 - 16.6)^2 + 20^2) = sqrt(0.6^2 + 20^2) = sqrt(0.36 + 400) = sqrt(400.36) ≈ 20.01 cm
3. Now, we can calculate the area of each triangular face using the formula: 0.5 * base * height, where the base is the length of the bottom edge of the face, and the height is the slant height found above.
Area of each triangular face = 0.5 * 18 * 20.01 = 180.09 cm²
4. Since there are 4 triangular faces, the total surface area of the pyramid is:
360 (area of the base) + 4 * 180.09 (area of each triangular face) = 1,080 + 720.36 = 1,800.36 cm²
Therefore, the correct answer is:
A. 1,800.36 cm²
1. The base of the pyramid is a rectangle with dimensions of 20 cm by 18 cm. Therefore, the area of the base is 20 * 18 = 360 cm².
2. To find the area of the four triangular faces, we need to first calculate the slant height of the pyramid. Using the Pythagorean theorem, we have:
slant height = sqrt((17.2 - 16.6)^2 + 20^2) = sqrt(0.6^2 + 20^2) = sqrt(0.36 + 400) = sqrt(400.36) ≈ 20.01 cm
3. Now, we can calculate the area of each triangular face using the formula: 0.5 * base * height, where the base is the length of the bottom edge of the face, and the height is the slant height found above.
Area of each triangular face = 0.5 * 18 * 20.01 = 180.09 cm²
4. Since there are 4 triangular faces, the total surface area of the pyramid is:
360 (area of the base) + 4 * 180.09 (area of each triangular face) = 1,080 + 720.36 = 1,800.36 cm²
Therefore, the correct answer is:
A. 1,800.36 cm²