Find the area of the quadilateral whose vertices are A (0, 0), B (0, 10), C (8, 2) and D (8, 7) ?

CONCEPT:

Let A (x1, y1), B (x2, y2) and C (x3, y3) be the vertices of a Δ ABC, then area of Δ ABC = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{x_1}}&{{y_1}}&1\\ {{x_2}}&{{y_2}}&1\\ {{x_3}}&{{y_3}}&1 \end{array}} \right|\)

CALCULATION:

Given: A (0, 0), B (0, 10), C (8, 2) and D (8, 7) are the vertices of a quadilateral ABCD

Here, we have to find the area of quadilateral ABCD

Area of quadilateral ABCD = Area of ΔABC + Area of Δ ACD

Let's find out the area of ΔABC

∵ A (0, 0), B (0, 10), C (8, 2) are the vertices of ΔABC

As we know that, if A (x1, y1), B (x2, y2) and C (x3, y3) be the vertices of a Δ ABC, then area of Δ ABC = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{x_1}}&{{y_1}}&1\\ {{x_2}}&{{y_2}}&1\\ {{x_3}}&{{y_3}}&1 \end{array}} \right|\)

⇒ Area of Δ ABC = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{0}}&{{0}}&1\\ {{0}}&{{10}}&1\\ {{8}}&{{2}}&1 \end{array}} \right|\)