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


4. The diameter of the wheel of a vehicle is 5 metre. It makes 7 revolutions per 9 seconds. What is speed of the vehicle in km/h?
Radius of the wheel = 52 metre
Distance covered in 1 revolution = Circumference of the wheel = 2πr = 2 x 227×52 metre

Therefore, Distance covered in one second = 2 x 227×52×79 metre

Therefore, Speed per hour = 2 x 227×52×79×185 = 44 km/h

5. The perimeter of a rhombus is 60 cm and one of its diagonal is 24 cm. Find the other diagonal of the rhombus.
Let ABCD is the rhombus whose diagonals BD and AC intersecting at point 'O'.
Side of rhombus = 14 x Perimeter = 14 x 60 = 15 cm.
Let BD = 24 cm
Then, BO = 12BD = 12 cm
Now, AO = AB2−BO2−−−−−−−−−√=152−122−−−−−−−√ = 9
Therefore, AC = 2 AO = 2 x 9 = 18 cm