Question

Find the area of the quadrilateral formed by joining the points (–4, 4), (–6, 0), (–4, –4), (–2, 0)


A).12 sq. units


B).16 sq. units


C).20 sq. units


D).32 sq. units

Answer 1

Step-by-step explanation:

answers is 16 units

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Answer 2

The area of the quadrilateral formed by joining the given points is 16 sq. units.

Given,

Coordinates of 4 points to be joined to form a quadrilateral:

(–4, 4), (–6, 0), (–4, –4), (–2, 0).

To find,

Area of the quadrilateral formed.

Solution,

We can see that here, the coordinates of four points are given as

(–4, 4), (–6, 0), (–4, –4), (–2, 0).

A quadrilateral is to be formed by joining the above points.

Now, let's plot the given points on the coordinate axes, and join them.

Refer figure.

The given points are represented by A, B, C, and D. On join the points to obtain quadrilateral ABCD.

It can be observed from the figure, that the quadrilateral thus obtained is a rhombus.

The lengths of its diagonals here are,

AC = 8 units, and

BD = 4 units.

We know that the area of a rhombus is given by

$A = \frac{1}{2} \times d_1d_2$

So, for the obtained quadrilateral ABCD,

$A = \frac{1}{2} \times AC \times BD$

$\implies A = \frac{1}{2} \times 8 \times 4$

$\implies A = \frac{32}{2}$

⇒ A = 16 unit².

Therefore, the area of the quadrilateral formed by joining the given points is 16 sq. units.

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