Question

Find the area of a quadrilateral ABCD having vertices at $$A(1, 2), B(1, 0), C(4, 0)$$ and $$D(4, 4)$$.

Answer 1

$$\textbf{Step 1 : Drawing a quadrilateral ABCD and writing their vertices. }$$

$$\text{In a quadrilateral ABCD we got a right angle triangle AXD and a rectangle ABCX}$$

$$\text{the given vertices are ,}$$

$$\text{A = (1,2)}$$

$$\text{B = (1 , 0)}$$

$$\text{C = (4 , 0)}$$

$$\text{D = (4 , 4)}$$

$$\textbf{Step 2 : Determining the Coordinates of X .}$$

$$\mathbb{X =(k , m)= {\huge(}\dfrac{4+4}{2} , \dfrac{4+0}{2}{\huge)}.................}$$$$\text{D - X - C}$$

$$\mathbb{X = (4 , 2)}$$

$$\textbf{Step 3 : Determining Area of }$$$$\mathbf{\Delta AXD.}$$

$$A(\Delta AXD) = \dfrac{1}{2} \times base \times height$$

$$ = \dfrac{1}{2} \times 3 \times 2$$

$$ = 3 \ sq.unit$$

$$\textbf{Step 4 : Determining Area of Rectangle ABCX}$$

$$A(\Box ABCX) = length \times breadth$$

$$=3 \times 2$$

$$=6 sq.unit$$

$$\textbf{Step 5 : Determining Area of quadrilateral ABCD .}$$

$$A(\Box ABCD) = A(\Delta AXD) + A(\Box ABCX)$$

$$=3 + 6$$

$$= 9 sq.unit$$

$$\textbf{Hence , Area of Quadrilateral is 9 sq.unit}$$