Q&A for How to Find the Surface Area of a Pyramid

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How do you find the lateral area of hexagonal pyramid, given the height and length of each side?

Community Answer

Use the base times height for the rectangles, and the altitude times base of the hexagonal face times three.

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Question

How would you calculate the surface area of pyramid that does not have a square base?

Community Answer

Use the formula (p x h/2) + (B), where p is the perimeter of the base, h is the slant height of the pyramid, and B is the area of the base. Below are some articles on finding the area of a pentagon and hexagon, two common pyramid bases: http://www.wikihow.com/Find-the-Area-of-a-Pentagon http://www.wikihow.com/Calculate-the-Area-of-a-Hexagon

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How do I double the lateral surface area of a square pyramid?

Donagan

Top Answerer

One way would be to double either the length of the sides of the base or the slant height (but not both).

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Question

Where does the height fit in?

Donagan

Top Answerer

The actual height of a pyramid does not factor in to the calculation of its surface area. However, the "slant height" does, being one of the dimensions of a pyramid's slanted surface (along with the width of the base).

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Question

A regular square pyramid is 3 m. Height and the perimeter of its base is 16 m. How do I find the volume of the pyramid?

Donagan

Top Answerer

V = (s)²(h) / 3, where s is the length of one side of the base, and h is the pyramid's height. The side of a square is 1/4 of the perimeter, so this pyramid has a base side of 4. Therefore, V = (4)²(3) / 3 = 16 cubic meters.

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Question

What if I'm only given the lateral surface area?

Donagan

Top Answerer

That's not enough information to find the total surface area (including the base area).

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What if I do not know the height?

Donagan

Top Answerer

If you don't know either the height or the slant height of a pyramid, you cannot determine the surface area.

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Question

How would I write the total surface area of a square-based pyramid having base side x cm and slant height y cm?

Donagan

Top Answerer

See Method 2 Step 1 above. Substitute x for b and y for h.

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How do I calculate the surface area of a triangle pyramid? Is it the same kind of mathematical equation, or something different?

Donagan

Top Answerer

If it's an equilateral triangle, it qualifies for Method 1 above. Otherwise, you would have to calculate the areas of each of the surfaces separately and add them together.

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How do I find the surface area of a heptagonal prism?

Donagan

Top Answerer

Assuming regular heptagonal bases, and lateral sides perpendicular to the bases, you would multiply an edge of the base by the height, and multiply by seven to find the total lateral surface area. If desired, add the areas of the bases. (The area of one base is half the product of the perimeter and the apothem.)

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What is the area of solid figures?

Donagan

Top Answerer

See Find Surface Area . If you're asking about volume, see Calculate Volume .

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Question

Why do you not use the height? The surface area of a triangle is half base x height...

Donagan

Top Answerer

We're talking about two different heights. The height of a pyramid is not the same thing as the height of any of its triangular surfaces. That height is called the "slant height," and that's the height used in measuring a pyramid's surface area. (The difference is that the height of a pyramid and the slant height of a surface area are not measured parallel to each other.)

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