Find a formula for the area of each figure in terms of s.

Question

Accepted Answer

Welcome back. Everyone. In this problem, we have a 30 60 90 degree triangle for which we want to write a formula for its area. A in terms of M, for our answer choices, A says that its area is three divided by two multiplied by M squared. B says it's two thirds of M squared. C says that it's a half of the square root of three multiplied by M squared. And D says that it's a third of the square root of two multiplied by M squared. Now, what do we know here? Well, we have a 30 60 90 triangle and that means that this is a right triangle. And in a right triangle, we can find its area by multiplying half of the base by the perpendicular height. OK. The perpendicular height of the triangle. And we have the perpendicular height of the triangle, the height at which the base and the height meet at 90 degrees. So in our triangle notice that our base is M multiplied by the square of three and our height is M. So that means then that its area is going to be equal to a half multiplied by the base M multiplied by a square of three multiplied by the height which is M. Now let's go ahead and solve M multiplied by the square of three multiplied by M equals the square of three multiplied by M squared. And in our denominator, it would have been two multiplied by one multiplied by one, which would simply be two. Therefore, our area of our triangle is the square of three divided by two multiplied by M squared. In terms of M, when we look back on our answer choices, that would have been answer choice. C thanks a lot for watching everyone. I hope this video helped.

Find a formula for the area of each figure in terms of s.

Key Concepts

Area of a Triangle

Semi-Perimeter

Heron's Formula

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