Area of Equilateral Triangle

In this page area of equilateral triangle we are going to see how to find the area of triangle. We have shown the formulas used to be find the area of the triangle, examples to understand this topic.

Formula:

     Area of Equilateral-triangle = (√3/4) a²

Here "a" represent the length of side of a triangle.

Example 1:

Find the area of the equilateral-triangle having the length of the side equals 10 cm

This problem can be done in two ways. We have shown those two methods one by one. In the first method we have used the above formula  to solve this problem. But in the second method we have used  the formula (1/2) x b x h to find the area.

Method 1:

Area of equilateral triangle = (√3/4) a²

Here a = 10 cm

                                    = (√3/4) (10)²

                                    = (√3/4) x (10) x (10)

                                     = (√3) x (5) x (5)

                                     =  25 √3 cm²


Method 2:

Here the side length 10 cm refers the measurement of each side of a triangle. Let us consider the triangle ABC. In this triangle the length of each side that is AB,BC and CA are measuring 10 cm

In the above triangle the measurement of the side DC is 5 cm. In the triangle ADC , the side AC is called hypotenuse side whose length is 10 cm.

So we can say AC² = AD² + DC²

                     10² = AD² + 5²

                    100 = AD² + 25

                    100 - 25 = AD²

                        AD² = 75

                       AD = √75

                       AD = 5√3

Now we can apply the formula to find the area of the triangle that is (1/2) x base x height

Here base is 10 cm and height is 5√3 cm

Area of the given triangle = (1/2) x 10 x 5√3

                                   =  5 x 5√3

                                   = 25√3  cm²   


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Area of Equilateral Triangle to Formulas for Shapes