Question

Find the area of the polygon.

Look at the picture please

A : 24.6 square units

B : 25.8 square units

C: 26.3 square units

D: 27.5 square units

Answer 1

Option D.

Explanation:

As we know area of a triangle =
`(1)/(2)* Base* Height`

1. Area of ΔJKL =
`(1)/(2)*(\text{Distance of L from base JK})* (JK)`

=
`(1)/(2)* (3)* (5)`

=7.5 square units

2. Area of ΔIJL =
`(1)/(2)*(\text{Distance of J from base IL})* (IL)`

=
`(1)/(2)* (3)* (5)`

= 7.5 square units

3. Area of triangle IKL =
`(1)/(2)*(\text{Distance of H from base IL})* (IL)`

=
`(1)/(2)* (5)* (5)`

=
`(25)/(2)=12.5` square units

Now area of ΔJKL + ΔIJL + ΔIKL = 7.5 + 7.5 + 12.5

= 27.5 square units

Option D. is the answer.

Answer 2

option D: 27.5 square units

Explanation:

Divide the polygon in 6 figures

see the attached figure

Area of figure 1 (right triangle)

A1=(1/2)(3)(3)=4.5 units²

Area of figure 2 (rectangle)

A2=(1)(3)=3 units²

Area of figure 3 (rectangle)

A3=(1)(3)=3 units²

Area of figure 4 (right triangle)

A4=(1/2)(3)(3)=4.5 units²

Area of figure 5 (right triangle)

A5=(1/2)(4)(5)=10 units²

Area of figure 6 (right triangle)

A6=(1/2)(1)(5)=2.5 units²

The total area is equal to

At=A1+A2+A3+A4+A5+A6

At=4.5+3+3+4.5+10+2.5=27.5 units²