Question

find area of the following polygon.​

Answer 1

$\huge{\underbrace{\underline{\color{magenta}{\bf{Solution:-}}}}}$

As we can see, the polygon ABCDEF is made from 4 triangles i.e. △ABF,△BFC,△FDC and △FDE .

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

As per the attached figure:

For △ABF , FB is the base and AG is the height.

For △BFC ,FC is the base and HB is the height.

For △FDC , FC is the base and DI is the height.

For △FDE ,FD is the base and EJ is the height.

$\begin{gathered}\text {The required area = }(\frac{1}{2} \times 6.5 \times 2) + (\frac{1}{2} \times 7 \times 4) + (\frac{1}{2} \times 7 \times 4) + (\frac{1}{2} \times 5 \times 2) \\\Rightarrow 6.5 + 14 + 14 +5\\\Rightarrow 39.5 \text{ cm}^{2} \\\end{gathered}$

Hence the area of polygon is 39.5 cm²

Answer 2

Question-

Find the area of the following polygon.

Answer-

This question seems very hard at first sight. It isn't a regular polygon. It is an irregular polygon. But, if you look closely, the polygon is divided into many triangles. So,

the area of the polygon ABCDEF = Total area of the triangles within it.

The formulae to keep in mind is the formulae to calculate the area of the triangle- 1/2 × b × h, where b and h are base and height respectively.

We need to find the area of all the triangles. The triangles whose area we have to find are-

• △ABF
• △BCF
• △CDF
• △DEF

Now that we know this, let us start solving.

1. Area of △ABF

Base = 6.5 cm

Height = 2 cm

Area = 1/2 × base × height

= 1/2 × 6.5 × 2

= 6.5 cm²

2. Area of △BCF

Base = 7 cm

Height = 4 cm

Area = 1/2 × base × height

= 1/2 × 7 × 4

= 7 × 2

= 14 cm²

3. Area of △CDF

Base = 7 cm

Height = 4 cm

Area = 1/2 × base × height

= 1/2 × 7 × 4

= 7 × 2

= 14 cm²

4. Area of △DEF

Base = 5 cm

Height = 2 cm

Area = 1/2 × base × height

= 1/2 × 5 × 2

= 5 cm²

Now that we have found out the area of these four triangles, we can find the area of the polygon.

Area of Polygon = Area of △ABF + Area of △BCF + Area of △CDF + Area of              △DEF

⇒ Area of Polygon = 6.5 cm² + 14 cm² + 14 cm² + 5 cm²

⇒ Area of Polygon = 39.5 cm²

Thus, the area of the polygon ABCDEF is 39.5 cm²