Find the area of the quadrilateral $ABCD$ , whose vertices are $A (− 3, − 1), B (− 2, − 4)$ $C (4, − 1)$ and $D (3, 4) .$

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answer is A.

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Detailed Solution

It is given that in quadrilateral ABCD the vertices are

A (− 3, − 1), B (− 2, − 4)

C (4, − 1)

and

D (3, 4) .

To find the area of the quadrilateral ABCD we have to find the area of the two triangles that join to form the quadrilateral ABCD.
We can find the area of the triangle we have to use the formula for area of a triangle which is

12 x 1 y 2 − y 3 + x 2 y 3 − y 1 + x 3 y 1 − y 2

.
Area of ΔABC

⇒ 12 x 1 y 2 − y 3 + x 2 y 3 − y 1 + x 3 y 1 − y 2 ⇒ 12 − 3 − 5 + 45 + − 2 0 ⇒ 352

Area of ΔABC

⇒ 12 x 1 y 2 − y 3 + x 2 y 3 − y 1 + x 3 y 1 − y 2 ⇒ 12 − 3 + − 2 0 + 43 ⇒ 212

To find the area of quadrilateral we can use the formula given below.
Area of ABCD = area of ΔACD + area of ΔABC.

⇒ 352 + 212 ⇒ 562 ⇒ 28

The area of the quadrilateral is 28

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.
Hence, the correct option is 1.

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