The perimeter of an isosceles triangle is 36 cm. If one of the equal sides is 13 cm, what is the area of the triangle?
Answer (2)
The area of the isosceles triangle, with a perimeter of 36 cm and equal sides of 13 cm, is calculated to be 60 cm². This is determined by first finding the base and height, then using the area formula for triangles. The final area is computed as 60 cm².
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To find the area of the isosceles triangle, we need to first understand its dimensions based on the given information.
Understanding the Triangle's Sides:
It's given that the perimeter is 36 cm.
In an isosceles triangle, two sides are equal. Let's label these equal sides as a , where a = 13 cm.
The perimeter formula for a triangle is: 2 a + b = 36 where b is the base of the triangle.
Plugging the values in, we have: 2 ( 13 ) + b = 36 26 + b = 36 b = 10 cm
Calculating the Area:
The area A of a triangle can be found using the formula: A = 2 1 × base × height
We need to find the height ( h ) of the triangle. In an isosceles triangle, if we draw a height from the apex perpendicular to the base, it splits the base into two equal parts. So each part will be 2 10 = 5 cm.
Using the Pythagorean theorem in one of the two right triangles formed, we have: h 2 + 5 2 = 1 3 2 h 2 + 25 = 169 h 2 = 144 h = 12 cm
Now that we have the height, we can calculate the area: A = 2 1 × 10 × 12 = 60 cm 2
Therefore, the area of the triangle is 60 cm 2 .
