Perimeters and Areas of Plane Figures

Mensuration is the part of geometry concerned with ascertaining lengths, areas, and volumes. Perimeter is the distance around a closed figure while area is the part of plane or region occupied by the closed figure.

1. Triangle

Sides: a, b, c

Perimeter = a + b + c

Area Δ = 1/2 × Base × Corresponding height

$$ \Delta = \sqrt{s(s - a)(s - b)(s - c)} $$

2. Rectangle

Length (l), Breadth (b)

Perimeter = 2(l + b)

Area = l × b

3. Square

Side: a

Perimeter = 4a

Area = a2

4. Parallelogram

Perimeter = 2(a + b)

Area = Base × Corresponding height = bh

5. Trapezium

Perimeter = a + b + c + d

Area = (half the sum of parallel sides) × height = ½(a + b)h

6. Rhombus

Perimeter = 4a

Area = ½ × d1 × d2

7. Circle

Radius: r

Circumference = 2πr

Area = πr2 

8. Sector of Circle

$$ \text{Perimeter} = \frac{2 \pi r}{360} \times \theta $$

$$ \text{Area} = \frac{\pi r^2}{360} \times \theta $$