ACT Math : How to find the area of an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 :Acute / Obtuse Isosceles Triangles

What is the area of an isosceles triangle with a vertex ofdegrees and two sides equal to?

Possible Answers:

Correct answer:

Explanation:

Based on the description of your triangle, you can draw the following figure:

_tri71

You can do this because you know:

  1. The two equivalent sides are given.
  2. Since a triangle isdegrees, you have onlyordegrees left for the two angles of equal size. Therefore, those two angles must bedegrees anddegrees.

Now, based on the properties of an isosceles triangle, you can draw the following as well:

_tri72

Based on your standard referencetriangle, you know:

Therefore,is.

This means thatisand the total base of the triangle is.

Now, the area of the triangle is:

or

Example Question #1 :How To Find The Area Of An Acute / Obtuse Isosceles Triangle

An isosceles triangle has a height ofand a base of. What is its area?

Possible Answers:

Correct answer:

Explanation:

Use the formula for area of a triangle:

Example Question #1 :Acute / Obtuse Isosceles Triangles

An isosceles triangle has a base length ofand a height that is twice its base length. What is the area of this triangle?

Possible Answers:

Correct answer:

Explanation:

1. Find the height of the triangle:

2. Use the formula for area of a triangle:

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