Area Formula for Quadrilaterals

Quadrilateral is a closed figure that has four sides in it. The interior angles add up to 360 degrees.  Also opposite sides are parallel and opposite angles are equal. Quadrilaterals can be classified into different types some of them are square, rectangle, parallelogram, rhombus and trapezoid. Five different formulas are used to calculate the area of quadrilateral. In parallelogram adjacent sides are of unequal lengths and angles are oblique (not right angles). A rectangle all four angles are right angles. An equivalent condition is that the diagonals bisect each other and are equal in length.

Area formula of Quadrilaterals


Area of a Square = $Side^{2}$
Area of a Kite = $\frac{1}{2}$diagonal
Area of a Parallelogram = base $\times$ height
Area of a Rectangle = base $\times$ height
Area of a Trapezoid = \[\frac{base_{1}+base_{2}}{2}height\]

Solved Examples

Question 1: Find the area of a trapezoid with bases of 11 inches and 12 inches, and a height of 5 inches.

Given $b_{1}$ = 11 inches
$b_{2}$ = 12 inches
h = 5 inches

Area of Trapezoid = $\frac{base_{1}+base_{2}}{2}$ $\times$ $Hieght$
= $\frac{11+12}{2}$ $\times$ 5
$\frac{23}{2}$ $\times$ 5
= $57.5 in^{3}$

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