To find the surface area of a rectangular pyramid, we need to calculate the areas of each face and then sum them up.
The formula for the surface area of a rectangular pyramid is:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Let's calculate the surface area step by step:
1. Base Area:
The base of the pyramid is a rectangle, so the base area is length * width.
Base Area = 15 m * 12 m = 180 m²
2. Slant Height:
To find the slant height, we can use the Pythagorean theorem.
h² = l² + w²
10² = 15² + 12²
100 = 225 + 144
100 = 369
Since the square root of 369 is not a whole number, we can't express the slant height exactly. However, we can use a calculator or a decimal approximation:
Slant Height ≈ √369 ≈ 19.23 m (rounded to the nearest hundredth)
3. Perimeter of Base:
The perimeter of a rectangle is given by 2 * (length + width).
Perimeter of Base = 2 * (15 m + 12 m) = 2 * 27 m = 54 m
4. Surface Area:
Finally, we can plug the values into the formula to calculate the surface area:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
= 180 m² + (0.5 * 54 m * 19.23 m)
= 180 m² + 519.21 m²
= 699.21 m²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is approximately 699.21 m². So the answer of 504.93 is incorrect.
Find the surface area of a rectangular pyramid with these measurements: l
= 15 m, w
= 12 m, and h
= 10 m. Express your answer as a decimal rounded to the nearest hundredth. the answer is 504.93
3 answers
No it is 504.93
I apologize for the confusion. Let's calculate the surface area of the rectangular pyramid again:
1. Base Area:
Base Area = 15 m * 12 m = 180 m²
2. Slant Height:
Using the Pythagorean theorem:
h² = l² + w²
10² = 15² + 12²
100 = 225 + 144
100 = 369
Slant Height ≈ √369 ≈ 19.23 m (rounded to the nearest hundredth)
3. Perimeter of Base:
Perimeter of Base = 2 * (15 m + 12 m) = 2 * 27 m = 54 m
4. Surface Area:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
= 180 m² + (0.5 * 54 m * 19.23 m)
≈ 180 m² + 519.21 m²
≈ 699.21 m²
I apologize once again, but the calculated surface area is approximately 699.21 m², not 504.93 m².
1. Base Area:
Base Area = 15 m * 12 m = 180 m²
2. Slant Height:
Using the Pythagorean theorem:
h² = l² + w²
10² = 15² + 12²
100 = 225 + 144
100 = 369
Slant Height ≈ √369 ≈ 19.23 m (rounded to the nearest hundredth)
3. Perimeter of Base:
Perimeter of Base = 2 * (15 m + 12 m) = 2 * 27 m = 54 m
4. Surface Area:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
= 180 m² + (0.5 * 54 m * 19.23 m)
≈ 180 m² + 519.21 m²
≈ 699.21 m²
I apologize once again, but the calculated surface area is approximately 699.21 m², not 504.93 m².