Important Questions of Mensuration: Quantitative Aptitude Mensuration is one the toughest topic of quantitative aptitude section. The only thing is it

Examples with Solution

Example1: What will be the area and perimeter of triangular plot whose sides are 17 m, 8m and 15m long?
Solution: Firstly, we will check which kind of triangle it is. Since, $8^2+{15}^2={17}^2.......(H^2=P^2+B^2)64+225=289=289$

Therefore, given triangle is a right angle triangle with: Hypotenuse $={17}^2$ Base or Perpendicular $=8$ or 15

Next thing we need is: Formula of Area and perimeter Area of triangle $=1/2$ Basetimes perpendicular $\Rightarrow 1/28\times 15\Rightarrow 60m^2$
Also, Perimeter $=8+15+17=40m$
Example2: What will be the area of equilateral triangle whose side is 4 cm.
Solution: Very simple question. You just need formula of area of equilateral triangle ( Equilateral triangle whose sides are equal)  

Area of equilateral triangle $=\sqrt{3}/4\times (side{)}^2\Rightarrow \sqrt{3}/4\times 4^2\Rightarrow 4\sqrt{3}c{m}^2$
Example3: The radius of a circle is 6cm. What is radius of another circle whose area is 36 times that of first? 
Solution: We know that, Area is directly proportional to square of radius $\Rightarrow (\text{Area of 2nd})/(\text{Area of 1st})=(\text{Radius of 2nd}{)}^2/(\text{Radius of 1st}{)}^2\Rightarrow 36/1=(\text{Radius of 2nd}{)}^2/36\Rightarrow \text{Radius}=36m$
Example4: One brick measures $30cm\times 20cm\times 15cm$ How many bricks will be required for a wall 30m times 2m times 1.5m?
Solution: Obviously, Number of bricks = (Total  volume  of  wall) / (volume  of  1  brick)
Note: Units should be same
Number of bricks $=(30\times 2\times 1.5\times 100\times 100\times 100)(30\times 20\times 15)\Rightarrow 10000$ bricks.
Example5: Surface area of cube is $150c{m}^2$. Find its volume and diagonal.
Solution: Surface area of cube $=6a^2=150\Rightarrow a=5cm$ Now, Volume of cube $=a^3=5^3=125c{m}^3$
Diagonal $=a\sqrt{3}=5\times \sqrt{3}\Rightarrow 8.66cm$