### 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 \(\Rightarrow 1/2 8 \times 15 \Rightarrow 60 m^{2}\)

Also, Perimeter \(= 8 +15 + 17 = 40 m\)

**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 \(= \sqrt{3}/4 \times (side)^{2} \Rightarrow \sqrt{3}/4 \times {4}^{2} \Rightarrow 4 \sqrt{3} cm^{2}\)

**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 \(\Rightarrow (\text{Area of 2nd})/ (\text{Area of 1st}) = (\text{Radius of 2nd})^{2}/ (\text{Radius of 1st})^{2} \Rightarrow 36/1 = (\text{Radius of 2nd})^{2}/ 36 \Rightarrow \text{Radius} = 36 m\)

**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 \(150cm^{2}\). Find its volume and diagonal.

**Solution:** Surface area of cube \(= 6 a^{2} = 150 \Rightarrow a = 5cm\) Now, Volume of cube \(= a^{3} = 5^{3} = 125cm^{3}\)

Diagonal \(= a \sqrt{3} = 5 \times \sqrt{3} \Rightarrow 8.66cm\)