Question

Find the area of the pentagonal field shown alongside. All dimensions are in metres

Answer 1

hopefully it helps you

Answer 2

Given:

The figure.

To find:

The area of the pentagonal field shown alongside

Solution:

We know that,

$\text{Area of a triangle}=\dfrac{1}{2}\times base\times height$

So,

$\text{Area of }\Detla ABG=\dfrac{1}{2}\times 50\times 80=2000$

$\text{Area of }\Detla BCG=\dfrac{1}{2}\times 50\times 70=1750$

$\text{Area of }\Detla CDF=\dfrac{1}{2}\times 20\times 30=300$

$\text{Area of }\Detla AEH=\dfrac{1}{2}\times 30\times 50=750$

We know that,

$\text{Area of trapezoid}=\dfrac{a+b}{2}\times h$

where, a and b are parallel sides and h is height.

So,

$\text{Area of trapezoid }DEHF=\dfrac{20+30}{2}\times 70$

$\text{Area of trapezoid }DEHF=\dfrac{50}{2}\times 70$

$\text{Area of trapezoid }DEHF=25\times 70$

$\text{Area of trapezoid }DEHF=1750$

Now,

$\text{Total area}=\text{Area of }\Detla ABG+\text{Area of }\Detla BCG+\text{Area of }\Detla CDF+\text{Area of }\Detla AEH+\text{Area of trapezoid }DEHF$

$\text{Total area}=2000+1750+300+750+1750$

$\text{Total area}=6550$

Therefore, the area of the pentagonal field is 6550 sq. metres.