Question

if A( -4,8) B( -3,-4) C (0,-5) and D( 5,6 )are the vertices of a quadrilateral abcd find its area

Answer 1

Answer:

Area = 72

Step-by-step explanation:

The shoelace formula or shoelace algorithm is used to compute the area of a simple polygon whose vertex are known in the cartesian coordinates in the plane.

The method requires us to make a table with the ordered pairs (x,y) of each vertex in strict order in the polygon in either direction (clockwise or counter-clockwise). Then we find the cross-product of each pair of points and sum all the products. The total area of the polygon in half the absolute value of the sum.

Let's form the table with the points in clockwise direction ADCBA. We must repeat the first vertex at the end.

$\begin{vmatrix}-4 &8 \\ 5 &6 \\0 &-5 \\-3 &-4 \\-4 &8 \end{vmatrix}$

Now we compute the cross-products, like 2x2 determinants:

-4*6-5*8=-64

5*(-5)-0*6=-25

0*(-4)-(-3)*(-5)=-15

(-3)*8-(-4)*(-4)=-40

The sum of all the products is

$-64-25-15-40=-144$

The required area is

$\displaystyle A=\frac{|-144|}{2}=72$

$\boxed{Area = 72}$