# AREA OF QUADRILATERALS WORKSHEET WITH ANSWERS

Area of quadrilaterals worksheet with answers is much useful to the students who would like to practice problems on quadrilaterals.

Before we look at the worksheet, first let us look at some basic stuff about area of quadrilateral when four vertices are given.

Let us consider the figure given below.

In the above quadrilateral, A(x₁, y₁), B(x₂, y₂), C(x₃, y₃) and D(x₄, y₄) are the vertices.

To find area of the quadrilateral ABCD, now we have take the vertices A(x₁, y₁), B(x₂, y₂), C(x₃, y₃) and D(x₄, y₄)  of the quadrilateral ABCD in order (counter clockwise direction) and write them column-wise as shown below.

And the diagonal products x₁y₂, x₂y₃, x₃y₄ and x₄y as shown in the dark arrows.

Also add the diagonal products xy, xy₂, x₄y₃ and x₁y₄ as shown in the dotted arrows.

Now, subtract the latter product from the former product to get area of the quadrilateral ABCD.

Hence, area of the quadrilateral ABCD is

=  (1/2) x { (x₁y₂+x₂y₃+x₃y₄+x₄y₁) - (xy₁+xy₂+x₄y₃+x₁y₄) }

## Area of quadrilaterals worksheet - Problems

Find the area of the quadrilaterals whose vertices are

(i)  (-4, -2), (-3, -5), (3, -2) and (2, 3)

(i)  (6, 9), (7, 4), (4, 2) and (3, 7).

(ii)  (-3, 4), (-5, -6), (4, -1) and (1, 2)

(iii)  (-4, 5), (0, 7), (5, -5) and (-4, -2)

## Area of quadrilaterals worksheet - Answers

Problem 1 :

Find the area of the quadrilateral whose vertices are (-4, -2), (-3, -5), (3, -2) and (2, 3)

Solution :

Plot the given points in a rough diagram as given below and take them in order (counter clock wise)

Let the vertices be A(-4, -2), B(-3, -5), C(3, -2) and (2, 3)

Then, we have

(x₁, y₁)  =  (-4, -2)

(x₂, y₂)  =  (-3, -5)

(x₃, y₃)  =  (3, -2)

(x, y)  =  (2, 3)

Area of triangle ABC is

=  (1/2) x { (x₁y₂+x₂y₃+x₃y₄+x₄y₁) - (xy₁+xy₂+x₄y₃+x₁y₄) }

=  (1/2) x  { [20 + 6 +9 - 4] - [6 - 15 -4 -12] }

=  (1/2) x  { [31] - [-25] }

=  (1/2) x  { 31 + 25 }

=  (1/2) x  { 56 }

=  28 square units.

Hence, are of triangle ABC is 28 square units.

As we have solved problem (i), we can solve the remaining three problems and get answer.

Answers for questions (ii), (iii) and (iv):

(ii)  17 square units.

(iii)  43 square units

(iiii)  60.5 square units

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