Introduction

Perimeter

It is the outside boundary of any closed shape. To find the perimeter we need to add all the sides of the given shape.

The perimeter of a rectangle is the sum of its all sides.

Perimeter = 3 + 7 + 3 + 7 cm

Perimeter of rectangle = 20 cm

Area

Area of any closed figure is the surface enclosed by the perimeter. Its unit is square of the unit of the length.

Area of a triangle

To find the area of a triangle, if the height is given, is

Area of triangle =\dfrac{1}{2}\times\text{base}\times\text{height}

Area of a Right Angled Triangle

Here base = 3 cm and height = 4 cm

Area of triangle =\dfrac{1}{2}\times3\times4=6\ \text{cm}^2

Area of Equilateral Triangle

If all the three sides are equal then it is said to be an equilateral triangle.

In the equilateral triangle, first, we need to find the height by making the median of the triangle.

If we take the midpoint of BC then it will divide the triangle into two right angle triangle.

Now we can use the Pythagoras theorem to find the height of the triangle.

\mathrm{AB^2=AD^2+BD^2}

\mathrm{(10)^2=AD^2+(5)^2}

\mathrm{AD^2=(10)^2-(5)^2}

\mathrm{AD^2=100-25=75}

\mathrm{AD=5\sqrt3}

Now we can find the area of triangle by

Area of triangle =\dfrac{1}{2}\times\text{base}\times\text{height}

=\dfrac{1}{2}\times10\times5\sqrt3

25\sqrt3\ \text{cm}^2

Area of Isosceles Triangle

In the isosceles triangle also we need to find the height of the triangle then calculate the area of the triangle.

 \begin{array}{l} \text { Height }=\sqrt{8^{2}-2^{2}} \\=\sqrt{64-4} \\ =\sqrt{60}=2 \sqrt{15} \\ \text { Area of triangle }=\frac{1}{2} \times \text { base } \times \text { height } \\  \begin{aligned} &=\frac{1}{2} \times 4 \times 2 \sqrt{15} \\=4 \sqrt{15} \mathrm{~cm}^{2} \end{aligned} \end{array}

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