What is the area of an isosceles triangle with side lengths 6, 6, and 4?

In summary, an isosceles triangle is a triangle with two equal sides and two equal angles. The formula for finding its area is A = 1/2 * b * h, where b is the length of the base and h is the height. The Pythagorean theorem can be used to find the height, and some real-life examples include the roof of a house and the design of a flag. An isosceles triangle is related to an equilateral triangle in that they both have congruent base angles and the height of an isosceles triangle is equal to the altitude of an equilateral triangle with the same side length.
  • #1
Elissa89
52
0
Side lengths are a=6, b=6, c=4. Find the area

A=1/2*b*h

I split the triangle in half to find the height. Since the base is 4, that divided the base into 2:

2^2+h^2=6^2

4+h^2=36

h^2=32

h=4*sqrt(2)
===========

1/2*4*4*sqrt(2)=area of 8*sqrt(2)

Did I do this correctly? I do not have an answer key to the study guide I was given.
 
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  • #2
Let's check your answer using Heron's formula...the semi-perimeter \(s\) is 8, hence:

\(\displaystyle A=\sqrt{8(8-6)(8-6)(8-4)}=\sqrt{2^7}=8\sqrt{2}\quad\checkmark\)
 

Related to What is the area of an isosceles triangle with side lengths 6, 6, and 4?

What is an isosceles triangle?

An isosceles triangle is a triangle with two equal sides and two equal angles. The base angles, which are the angles opposite the equal sides, are always congruent.

How do you find the area of an isosceles triangle?

The formula for finding the area of an isosceles triangle is A = 1/2 * b * h, where b is the length of the base and h is the height. The height can be found by using the Pythagorean theorem or by drawing an altitude from the apex to the base, creating two right triangles.

Can you use the Pythagorean theorem to find the area of an isosceles triangle?

Yes, you can use the Pythagorean theorem to find the height of an isosceles triangle, which can then be used to find the area. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

What are some real-life examples of isosceles triangles?

Some examples of isosceles triangles in real life include the roof of a house, the shape of a sail on a boat, and the design of a flag. They can also be found in the construction of bridges, buildings, and other structures.

What is the relationship between an isosceles triangle and an equilateral triangle?

An isosceles triangle is a special type of triangle in which two of the sides are equal, whereas an equilateral triangle is a special type of triangle in which all three sides are equal. However, both types have congruent base angles, and the height of an isosceles triangle is equal to the altitude of an equilateral triangle with the same side length.

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