Areas and Mensuration

1. If sides of a triangle are 8 cm, 15 cm and 17 cm respectively. Find its area.
Area of the triangle when all the three sides are given = s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√ where s=a+b+c2

s = 8+15+172 = 20 cm

Therefore, Area = 20×(20−8)×(20−15)×(20−17)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

= 20×12×5×3−−−−−−−−−−−−√
= 4×5×3×4×5×3−−−−−−−−−−−−−−−−−√ = 4 x 5 x 3 = 60 cm2
Trick:
The triangle is right angle triangle as 172=152+82
Therefore, Area of right angle triangle = 12 x 8 x 15 = 60 cm2

2. Two parallel sides of a trapezium are 4 cm and 5 cm respectively. The perpendicular distance between the parallel sides is 6 cm. Find the area of the trapezium.
Area of trapezium when height and two parallel sides are given = 12×h×(a+b) = 12 x 6 x (4 + 5) = 27cm2

3. If perimeter and area of a square are equal. Side of the square (in cm) is:
Given, (Side)2 = 4 x (Side)
Therefore, Side = 4 cm