Crystal Pyramid

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Crystal Pyramid

How do i solve this Trig exam question?

Question:

The shape of a perpendicular mineral is a double pyramid with 8 faces. Each face consists of an isosceles triangle whose base is 164pm and two equal base angles are 50 degrees. Find the surface area of the crystal

So a walkthrough of that question all the way to the answer please

Thanks alot

Hello!

Let it be known that the area of a triangle is 1/2(base)(height). We know the base of a triangle (164pm), so now we need the height.

To find the height, let us draw half of an isosceles triangle, so that it is a right triangle. The height can now be found by using Tangent:
Tan(50) = height / 82; 82 is 1/2 the base given, 164, and 50 is the degree given.

Solving this shows that the height is about 97.72pm. Now we can plug base and height into the equation
Area = 1/2(base)(height)
= 1/2 ( 164pm) (97.72pm)
= 8013.04 pm^2

Now, we have 8 sides, so the surface area is 8013.04*8 = 64104.32 pm^2

I hope this helps!

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Crystal Pyramid

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