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ISEE Upper Level Math : How to find the height of an eqilateral triangle

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Example Questions

Example Question #1 : How To Find The Height Of An Eqilateral Triangle

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

Possible Answers:

$3\ cm$

$4\ cm$

$4\sqrt{3}\ cm$

$2\sqrt{3}\ cm$

$3\sqrt{3}\ cm$

Correct answer:

$2\sqrt{3}\ cm$

Explanation:

$Area=\frac{1}{2}absinC$ ,

where and are the lengths of two sides and is the corresponding angle.

In an equilateral triangle, all of the sides have the same length, and all three angles are $60^{\circ}$ .

$Area=\frac{1}{2}absinC=\frac{1}{2}\times 4\times 4\times sin60^{\circ}$

$sin60^{\circ}=\frac{\sqrt{3}}{2}\Rightarrow Area=\frac{1}{2}\times 4\times 4\times \frac{\sqrt{3}}{2}=4\sqrt{3}\ cm^2$

Now plug this area into the alternate formula for the area of the triangle and solve for the height:

$Area =\frac{bh}2{}\Rightarrow 4\sqrt{3}=\frac{4\times h}{2}\Rightarrow h=2\sqrt{3}\ cm$

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Example Question #71 : Triangles

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

Possible Answers:

$\frac{8}{3}\ cm$

$\frac{8\sqrt{3}}{3}\ cm$

$4\ cm$

$\frac{4\sqrt{3}}{3}\ cm$

$8\ cm$

Correct answer:

$\frac{8\sqrt{3}}{3}\ cm$

Explanation:

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side.

We know that, in an equilateral triangle, all three angles measure $60^{\circ}$ .

$sin\angle A=\frac{h}{AB}=\frac{h}{c}$

$sin\angle A=\frac{h}{c}\Rightarrow sin60^{\circ}=\frac{4}{c}\Rightarrow \frac{\sqrt{3}}{2}=\frac{4}{c}\Rightarrow c=\frac{8}{\sqrt{3}}=\frac{8\sqrt{3}}{3} \ cm$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : How to find the height of an eqilateral triangle

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Height Of An Eqilateral Triangle

Example Question #71 : Triangles

All ISEE Upper Level Math Resources

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