# Area of a Triangle

## Formula

Area of triangle = (1/2) × "base" × "height" = 1/2 × b × h.

# Area of a triangle:

To get the area of the triangle, we first choose one of the sides to be the base (b). Then we draw a perpendicular line segment from a vertex of the triangle to the base. This is the height (h) of the triangle. The area of a triangle is equal to half the product of the base and the height.

Area of triangle = (1/2) × "base" × "height" = 1/2 × b × h

All the congruent triangles are equal in the area but the triangles equal in the area need not be congruent.

## Areas of different types of triangles:

Consider an acute and an obtuse triangle.

Area of each triangle = (1/2) × "base" × "height" = 1/2 × b × h

## Example

Find the area of the following triangle:

Area of triangle = 1/2bh

= 1/2 × QR × PS

= 1/2 × 4cm × 2cm

= 4 cm2

## Example

Find the area of the following triangle:

Area of triangle = 1/2bh

= 1/2 × MN × LO

= 1/2 × 3cm × 2cm

= 3 cm2

## Example

Find BC, if the area of the triangle ABC is 36 cm2 and the height AD is 3 cm.

Height = 3 cm, Area = 36 cm2

Area of the triangle ABC =1/2bh

36 = 1/2 × b × 3

b = (36 xx 2)/3 = 24 cm

So, BC = 24 cm.

## Example

In ∆PQR, PR = 8 cm, QR = 4 cm and PL = 5 cm.

Find:
(i) the area of the ∆PQR
(ii) QM.

(i) QR = base = 4 cm, PL = height = 5 cm

Area of the triangle PQR =1/2bh

= 1/2 xx 4 xx 5

= 10 cm2

(ii) PR = base = 8 cm, QM = height = ?, Area = 10 cm2

Area of triangle = 1/2 xx b xx h

10 = 1/2 xx 8 xx h

h = 10/4 = 5/2 = 2.5.

QM = 2.5 cm

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