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

Question

Accepted Answer

Welcome back. Everyone. In this problem, we have an equi angular triangle for which we want to write a formula for its area. A in terms of Q, for our answer choices, A says that its area is the square root of three divided by two, all multiplied by Q squared B says it's the square root of three divided by four, all multiplied by Q squared. C says that it's three divided by two multiplied by Q squared and A and D sorry says that it's 3/4 multiplied by Q squared. Now, what do we know here? Well, if we're going to find the area for this e angular triangle, which means that all its angles are equal, which as we see on the diagram, that also means all its sides are equal. We can use the formula that says the area of a triangle equals half A B sign theater. OK? Where A and B are two sides of the triangle and the theta is the angle that's formed between A and B. In other words, for our triangle, we'd be using these two sides and the angle that's between them. Now, the good thing is for our triangle, we know all of the angles and all of the sides. So really, we can use any two sides. So let's say that we use these two sides, Q and Q and the angle between them, which is 60 degrees, then this tells us that the area for a triangle will be equal to a half multiplied by a or one side which is Q multiplied by another side. Q multiplied by the sign of the angle between them, which is 60 degrees, no, Q multiplied by Q equals Q squared. And the sign of 60 degrees equals the square root of three divided by two. Now, we can multiply throughout notice that one multiplied by Q squared multiplied by the square of three equals the square of three multiplied by Q squared and two multiplied by two equals four. So the area for a triangle equals the square of three divided by four multiplied by Q squared. When we look on our list of answer choices that would have been answer choice. B 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 Formulas for Geometric Figures

Expressing Dimensions in Terms of a Variable

Trigonometric Relationships in Geometry

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