Find the Height of the Triangle, If Area of Triangle is 60 cm² and Base is 12 cm

Find the Height of the Triangle, If Area of Triangle is 60 cm² and Base is 12 cm

To find the height of a triangle given its area and base, you can use the formula for the area of a triangle.

Area = 1/2 x base x height

Area of the triangle = 60 cm²

Base of the triangle = 12 cm

Let the height of the triangle be h

Using the formula, we can set up the equation

60 = 1/2 x 12 x h

First, simplify the right side of the equation

60 = 6h

Next, solve for h,

h = 60/6

h = 10 cm

Therefore, the height of the triangle is 10 cm

How to Find the Height of a Triangle?

Finding the height of a triangle is a common geometric task. The height, also known as the altitude, is the perpendicular distance from the base to the opposite vertex. This measurement is crucial for various calculations, including determining the area of the triangle.

Area Calculation:

The height is essential for calculating the area of a triangle. The formula for the area of a triangle is 1/2 x base x height

This formula shows that knowing the height allows us to determine the triangle's area accurately.

Structural Analysis:

In construction and engineering, knowing the height of triangular components helps in analyzing the structural integrity and load distribution.

Trigonometry Applications:

The height of a triangle is used in various trigonometric calculations and problems. It helps in finding other dimensions and angles within the triangle.

Steps to Find the Height of a Triangle

Begin by knowing the base length and the area of the triangle. These values are necessary to calculate the height

Apply the area formula of a triangle,

Area = 1/2 x base x height

Solve for the height by rearranging the formula. The height can be found using

height = 2 x Area / base

Then assign the values of the base and the area into the rearranged formula to find the height.