Advertisement Remove all ads

Area of a Triangle

Advertisement Remove all ads

Topics

formula

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

notes

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

If you would like to contribute notes or other learning material, please submit them using the button below.

Shaalaa.com | Area of Triangle

Shaalaa.com


Next video


Shaalaa.com


Area of Triangle [00:13:58]
S
Series: Area of Triangle
0%


Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×