An isosceles triangle has a base that is 10 cm long and legs that are 13 cm long as shown . Use the Pythagorean theorem to find the height of the triangle
Answers
The formula for the area of a triangle is:
A = 1/2bh
The base of this isosceles triangle is given as 12cm.
Because the line which bisects and isosceles triangles is at a right angle to the base we can use the Pythagorean Theorem to find the height.
The Pythagorean Theorem states:
a² + b² = c²
Where:
"a" and "b" are sides of a right triangle.
"c" is the hypotenuse of a right triangle.
In this problem, the hypotenuse, or "c" , is 20cm
One side of the right triangle is the height which we need to solve for.
The other side of the right triangle for this isosceles
triangle is 1/2 of the base, or, 6cm
a² + (6cm²) = (20cm²)
a² + 36cm² = 400cm²
a² 36cm² - 36cm² = 400cm² - 36cm²
a² = 364cm²
√a² = √364cm²
a ≅ 19cm
Therefore the height is approximately: 19.08cm
We can now substitute into the formula for the area to determine the area of this triangle:
A = 1/2 × 12cm × 19cm
A = 114cm² accurate to the nearest square centimeter.
