To find the surface area of the rectangular pyramid, we need to find the area of the base and the area of the three lateral faces.
1. Area of the base:
Since the base is a rectangle, the area is given by:
Area = length × width
Area = 10 mm × 8 mm
Area = 80 mm²
2. Area of the three lateral faces:
The lateral faces are three rectangles. The area of a rectangle is given by:
Area = perimeter × height / 2
In this case, there are three rectangles with different heights (slant heights) and the same perimeter (10 + 8 + 12 + 15 = 45 mm).
For the lateral face with a slant height of 15 mm:
Area1 = 45 mm × 15 mm / 2
Area1 = 337.5 mm²
For the lateral face with a slant height of 12 mm:
Area2 = 45 mm × 12 mm / 2
Area2 = 270 mm²
For the lateral face with a slant height of 12 mm:
Area3 = 45 mm × 12 mm / 2
Area3 = 270 mm²
3. Total surface area:
Total surface area = area of the base + area of the three lateral faces
Total surface area = 80 mm² + 337.5 mm² + 270 mm² + 270 mm²
Total surface area = 957.5 mm²
Therefore, the surface area of the rectangular pyramid is 957.5 mm².
what is the surface area of the rectangular pyramid? The base is 8 mm. the length is 10. The two slant heights are 12 and 15 mm.
3 answers
wrong
My apologies for the mistake. Let's correct the calculation.
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = Base Area + (1/2) * Perimeter * Slant Height
Given:
Base length = 8 mm
Length = 10 mm
Slant heights: 12 mm and 15 mm
1. Base Area:
Base Area = 8 mm * 10 mm = 80 mm^2
2. Lateral faces:
a. For the slant height of 12 mm:
Perimeter = 2 * (8 mm + 10 mm) = 36 mm
Lateral Face Area = (1/2) * 36 mm * 12 mm = 216 mm^2
b. For the slant height of 15 mm:
Perimeter = 2 * (8 mm + 10 mm) = 36 mm
Lateral Face Area = (1/2) * 36 mm * 15 mm = 270 mm^2
3. Total Surface Area:
Total Surface Area = Base Area + Sum of Lateral Faces Area
Total Surface Area = 80 mm^2 + 216 mm^2 + 270 mm^2
Total Surface Area = 566 mm^2
Therefore, the surface area of the rectangular pyramid is 566 mm^2. Thank you for pointing out the error, and I appreciate your understanding.
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = Base Area + (1/2) * Perimeter * Slant Height
Given:
Base length = 8 mm
Length = 10 mm
Slant heights: 12 mm and 15 mm
1. Base Area:
Base Area = 8 mm * 10 mm = 80 mm^2
2. Lateral faces:
a. For the slant height of 12 mm:
Perimeter = 2 * (8 mm + 10 mm) = 36 mm
Lateral Face Area = (1/2) * 36 mm * 12 mm = 216 mm^2
b. For the slant height of 15 mm:
Perimeter = 2 * (8 mm + 10 mm) = 36 mm
Lateral Face Area = (1/2) * 36 mm * 15 mm = 270 mm^2
3. Total Surface Area:
Total Surface Area = Base Area + Sum of Lateral Faces Area
Total Surface Area = 80 mm^2 + 216 mm^2 + 270 mm^2
Total Surface Area = 566 mm^2
Therefore, the surface area of the rectangular pyramid is 566 mm^2. Thank you for pointing out the error, and I appreciate your understanding.
2 answers