Question

find the area of octagon​

Answer 1

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Area of Octagon Formula

=2(1+√2)a²

Side = 5Cm

A = 2 ( 1 + √2 ) 5²

A = 2 ( 1 + √2 ) 25

A = 2 ( 2.41 ) 25

A = 4.82 × 25

A = 120.5

Answer 2

Solution,

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The line segments CH and GD divide the octagon to 3 parts:

→ 2 trapeziums

→ 1 rectangle

We know the following values:

→ The line perpendicular to CH = 3 cm

→ The longer parallel line of the trapezium = 13 cm

→ The length of one side = 5 cm

Let's first consider one of the trapeziums!

✳ Trapezium

Area of a trapezium = $\mathtt{\dfrac{1}{2}\times (a+ b)\times h}$

Where, a and b are parallel opposite sides and h denotes the height.

Substituting the values:

= $\mathtt{\dfrac{1}{2}\times(5+13)\times3}$

= 27 cm²

→Area of two such trapeziums = 27 x 2

= 54 cm²

✳ Rectangle

Area of a rectangle = lb

Length = 13 cm

Breadth = 5 cm

Substituting the values:

= 13 x 5

= 65 cm²

→ Total area of octagon = Area of the 2 trapeziums + area of rectangle

= 54 + 65

= 119 cm²

∴ The area of the octagon is 119 cm².