Question

Find the area of a quadrilateral with diagonal $13m$and offsets $7m$and $3m$.

Answer 1

Hint:First, we need to know about the area of the quadrilateral.
Since the area is defined in any of the regions which include in particular the boundary and quadrilateral has four sides in that the region inside the four sides are known as the area of the quadrilateral.
It is measured in square units. And it has six types of quadrilaterals, any polygon with four sides is also called the area of the quadrilateral.

Formula used:
Area of the quadrilateral $ = \dfrac{1}{2} \times D \times S$.
where D is the diagonal and S is the sum of the given offsets (sum of the given perpendicular from the opposite vertices)

Complete step-by-step solution:
Since from the given that we have the area of a quadrilateral with diagonal is $13m$and thus $D = 13m$
Also, given that we have offsets $7m$and $3m$ we need to find the sum of these two to substitute into the given formula.
(From the addition operation we known that Addition is the adding or sum of two or more than two numbers and gets the new value)
Thus, the sum of the offsets (perpendicular from opposite vertices) is $7m + 3m$and thus we get $S = 10m$
Hence, we get the sum of the offsets and also the diagonal, so substitute every value into the formula of the Area of the quadrilateral $ = \dfrac{1}{2} \times D \times S$.
Thus, we get the Area of the quadrilateral $ = \dfrac{1}{2} \times D \times S \Rightarrow \dfrac{1}{2} \times 13m \times 10m$
With the help of multiplication and division operation, we have the Area of the quadrilateral $\dfrac{1}{2} \times 13m \times 10m = \dfrac{{130}}{2} \Rightarrow 65{m^2}$
Hence, we get, Area of the quadrilateral is $65{m^2}$

Note:While multiplying the values of the Area of the quadrilateral $ = \dfrac{1}{2} \times D \times S \Rightarrow \dfrac{1}{2} \times 13m \times 10m$also the meter times of meter gets meter square that is $m \times m = {m^2}$
In the quadrilateral, the sum of all interior angles is always ${360^0}$
There are six types of quadrilaterals (four sides) which are Square, Rectangle, Parallelogram, Rhombus, Trapezium, and Kite.
But, in squares only the sides are equal.