Question

Find the area of the polygon.

Answer 1

Answer:

option D: 27.5 square units

Step-by-step 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

Answer 2

Answer:

Option D.

Step-by-step explanation:

As we know area of a triangle = $\frac{1}{2}\times Base\times Height$

1. Area of ΔJKL = $\frac{1}{2}\times(\text{Distance of L from base JK})\times (JK)$

= $\frac{1}{2}\times (3)\times (5)$

=7.5 square units

2. Area of ΔIJL = $\frac{1}{2}\times(\text{Distance of J from base IL})\times (IL)$

=  $\frac{1}{2}\times (3)\times (5)$

= 7.5 square units

3. Area of triangle IKL = $\frac{1}{2}\times(\text{Distance of H from base IL})\times (IL)$

= $\frac{1}{2}\times (5)\times (5)$

= $\frac{25}{2}=12.5$ square units

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

= 27.5 square units

Option D. is the answer.