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Download now on Google PlayIn the earlier classes, we studied about perimeter and area of triangles.

**Perimeter**\(=\) \(\text{Sum of the three sides of the triangle}\)

**Area**\(=\) $\frac{1}{2}$ \(\times \ \text{Base} \times \text{Height}\)

Let us discuss how to find the area of different types of triangles in detail.

Area of a right angle triangle:

When the triangle is right angle triangle, we can directly apply the formula and can find the area. Because, right angle triangle have base and height.

Suppose \(AB = 6 \ cm\), \(BC = 8 \ cm\) and \(AC = 10 \ cm\).

Area \(=\) $\frac{1}{2}$ \(\times \ BC \times AB\)

Area \(=\) $\frac{1}{2}$ \(\times \ 8 \times 6\)

Area \(=\) \(24 \ cm^{2}\)

Area of an equilateral triangle:

To find the area of an equilateral triangle and isosceles triangle:

**Step 1**: Draw a perpendicular line from the top of the vertex to the base. This line divides the base into two equal halves. Also, divides the triangle into two triangles of equal area.

**Step 2**: To find the area, we need height \((AD)\). Using Pythagoras theorem, we can find height \((AD)\).

\( \text{Hypotenuse}^{2}\) \(=\) \(\text{Base}^{2}\) \(+ \text{Height}^{2}\)

**Step 3**: After finding \(AD\), we can find the area of \(\Delta ABD\).

**Step 4**: Since \(AD\) divides a \(\Delta ABC\) into two equal areas, area of \(\Delta ABD\) and area of \(\Delta ADC\) are same.

**Step 5**: Thus, adding area of \(\Delta ABD\) and \(\Delta ADC\), we get the area of \(\Delta ABC\).

Area of an isosceles triangle:

In the same way of finding the area of an equilateral triangle, we can find the area of an isosceles triangle.

Area of a scalene triangle:

For a scalene triangle, we cannot find the height, because all the three sides are different.

In this case, we have a formula called Heron's formula to find the area of triangles.

Important!

Heron's formula can be applied for all type of triangles.