Question

find the area of following polygon in figure 14.11​

Answer 1

Answer:

calculate the areas of all traingles one by one using formula 1/2×b×h

Answer 2

Answer:

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

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

2

1

×base×height

As per the attached figure:

For \triangle ABF△ABF , \text {FB}FB is the base and \text {AG}AG is the height.

For \triangle BFC△BFC , \text {FC}FC is the base and \text {HB}HB is the height.

For \triangle FDC△FDC , \text {FC}FC is the base and \text {DI}DI is the height.

For \triangle FDE△FDE , \text {FD}FD is the base and \text {EJ}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}

The required area = (

2

1

×6.5×2)+(

2

1

×7×4)+(

2

1

×7×4)+(

2

1

×5×2)

⇒6.5+14+14+5

⇒39.5 cm

2

Hence the area of polygon is 39.5\text{ cm}^{2}39.5 cm

2