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