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If b and h be the base and the height of the parallelogram,
respectively. Quick Check

1
Then, the area of a triangle = × (b × h) sq. units Take different parallelograms. Divide
2 each of the parallelograms into two
Look at the adjoining figure of an obtuse-angled triangle, triangles by cutting along any of its
the height of the obtuse-angled triangle is the perpendicular diagonals. Are the triangles congruent?
drawn from the vertex to the base which is outside the
triangle. A
So, the area of the adjoining obtuse-angled triangle ACB

1
= × AD × BC sq. units Height
2
In a right-angled triangle, the perpendicular side of the triangle is D C Base B
the height of the triangle.

1
So, the area of a right-angled triangle BAC = × (base × height) B
2

= 1 × AB × AC Height
2

Example 16: Find the area of the following triangles: A Base C
L

(a) 6 cm (b) 2 cm

8 cm O M 3 cm N

Solution: (a) Given that the base of triangle = 8 cm, and the height of the triangle = 6 cm
1
We have, area of triangle = (base × height)
2
1 1
= × (8 × 6) cm = × 48 cm 2
2
2 2
= 24 cm 2
The area of the triangle is 24 cm .
2
(b) Given that the base of DLMN, MN = 3 cm, and the height of the triangle, LO = 2 cm
1
We have, area of triangle = (base × height)
2
1
= × (3 × 2) cm
2
2
1
= × 6 cm 2
2
= 3 cm 2

2
\ Thus, the area of the triangle is 3 cm .

291 Perimeter and Area