Question

The rectangle has a width of x cm

The length of the rectangle is 8cm longer than the width

4 of these rectangles are used to make this 8 sided shape

The perimeter of the 8 sided shape is 90cm

Work out the area of the 8 sided shape !

Answer 1

Answer:

The Area of 8 shaped figure is 62.56 sq cm

Step-by-step explanation:

Given as :

The width of rectangle = W =  x cm

The length of rectangle = L= (x + 8) cm

Perimeter of rectangle = 2 × ( W + L )

Or, Perimeter of rectangle = 2 × ( x + x + 8 ) cm

i.e Perimeter of rectangle = 2 × ( 2 x + 8 ) cm               .........1

Area of rectangle = L × Width

i,e Area of rectangle = (x + 8) x

Or.  Area of rectangle = x² + 8 x   cm²                          .........2

Again

4 of these rectangle are used to make 8 sided shape

And Perimeter of 8 sided shape = 90 cm

So,

Perimeter of 8 sided shape = 4 × Perimeter of rectangle

Or, 90 cm = 4 ×  2 × ( 2 x + 8 ) cm

Or, 90 = 8 × ( 2 x + 8 )

Or, 90 = 16 x + 64

Or, 16 x = 90 - 64

or , 16 x = 26

i.e  x = $\dfrac{13}{8}$  = 1.625 cm

So, The width of rectangle = x = 1.625 cm

And The length of rectangle = x + 8 = 1.625 + 8 = 9.625 cm

So, Area of rectangle = L × W

i.e Area of rectangle = 9.625 cm × 1.625 cm = 15.64 sq cm

Again

Area of 8 shaped figure = 4 × area of each rectangle

i.e Area of 8 shaped figure = 4 × 15.64 sq cm

∴ Area of 8 shaped figure = 62.56 sq cm

Hence, The Area of 8 shaped figure is 62.56 sq cm Answer

Answer 2

Answer:

The Area of 8 shaped figure is 62.56 sq cm

Step-by-step explanation:

Given as :

The width of rectangle = W = x cm

The length of rectangle = L= (x + 8) cm

Perimeter of rectangle = 2 × ( W + L )

Or, Perimeter of rectangle = 2 × ( x + x + 8 ) cm

i.e Perimeter of rectangle = 2 × ( 2 x + 8 ) cm .........1

Area of rectangle = L × Width

i,e Area of rectangle = (x + 8) x

Or. Area of rectangle = x² + 8 x cm² .........2

Again

4 of these rectangle are used to make 8 sided shape

And Perimeter of 8 sided shape = 90 cm

So,

Perimeter of 8 sided shape = 4 × Perimeter of rectangle

Or, 90 cm = 4 × 2 × ( 2 x + 8 ) cm

Or, 90 = 8 × ( 2 x + 8 )

Or, 90 = 16 x + 64

Or, 16 x = 90 - 64

or , 16 x = 26

i.e x = \dfrac{13}{8}

8

13

= 1.625 cm

So, The width of rectangle = x = 1.625 cm

And The length of rectangle = x + 8 = 1.625 + 8 = 9.625 cm

So, Area of rectangle = L × W

i.e Area of rectangle = 9.625 cm × 1.625 cm = 15.64 sq cm

Again

Area of 8 shaped figure = 4 × area of each rectangle

i.e Area of 8 shaped figure = 4 × 15.64 sq cm

∴ Area of 8 shaped figure = 62.56 sq cm

Hence, The Area of 8 shaped figure is 62.56 sq cm Answer