6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale. 15m, 7.5 over 3m, 12m
862m3
540m2
1,125m2
647m2
The answer is C. 1125 m^2
Good luck everyone it’s rough out here for us who cheat, it’s so difficult to find answers for unit tests lol
It's hard to because they put the tests in different units and change the answers
6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is
I'm sorry, I cannot provide an answer without an accompanying image or description of the pyramid. Please provide more information or a visual.
6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale.
Without a provided image or description of the pyramid, I cannot provide an answer to this question. Please provide more information.
To find the surface area of a regular pyramid, we need to find the sum of the areas of all its faces.
First, let's identify the faces of the pyramid. A regular pyramid has one base, which is a regular polygon, and triangular faces that converge to a single vertex.
From the given information, we can identify that the base of the pyramid is a pentagon because it is a regular polygon with five sides. The height of the pyramid is given as 7.5 over 3m. We can assume that this is the slant height since it is not specified.
To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height, height, and half the length of the base form a right triangle. Let's calculate the slant height:
Using the Pythagorean theorem:
slant height^2 = height^2 + (1/2 * base)^2
slant height^2 = (7.5/3)^2 + (15/2)^2
slant height^2 = (2.5)^2 + (7.5)^2
slant height^2 = 6.25 + 56.25
slant height^2 = 62.5
slant height = √62.5
slant height ≈ 7.905 m (rounded to three decimal places)
Now that we have the slant height, let's calculate the surface area. The surface area of a regular pyramid can be calculated using the formula:
Surface area = base area + (1/2 * perimeter of base * slant height)
1. Base area:
The base of the pyramid is a pentagon, so we need to find its area. Since it is a regular pentagon, we can use the formula:
Base area = (5/4) * s^2 * cot(180°/5)
where s is the side length of the pentagon.
Given base side length = 15m
Base area = (5/4) * 15^2 * cot(180°/5)
Base area ≈ 191.783m² (rounded to three decimal places)
2. Perimeter of the base:
The base of the pyramid is a pentagon, so the perimeter is equal to 5 times the side length:
Perimeter = 5 * 15m
Perimeter = 75m
Now, we can calculate the surface area using the formula mentioned earlier:
Surface area = base area + (1/2) * perimeter of base * slant height
Surface area ≈ 191.783m² + (1/2) * 75m* 7.905m
Surface area ≈ 191.783m² + 296.625m²
Surface area ≈ 488.408m²
Rounded to the nearest whole number, the surface area of the regular pyramid is approximately 488m².
Therefore, the correct option is 647m².