Here is a rectangle which has a width of x cm. The length of the rectangle is 8cm longer than the width of the rectangle. 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.

Here is a rectangle which has a width of x cm The length of the rectangle is 8cm longer than the width of the rectangle 4 of these rectangles are used to make t class=

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Answer:

420 cm²

Step-by-step explanation:

Given the width is x then the length is x + 8 ( 8 longer than width )

Given the perimeter = 90 cm

Sum the lengths of the sides stating at the top left corner and going clockwise

Noting that the indentation small part is 8 - x

x + 8 + x + x + 8 - x + 8 + x + x + 8 + x + x + 8 - x + 8 + x

= 6x + 48

Equating perimeters

6x + 48 = 90 ( subtract 48 from both sides )

6x = 42 ( divide both sides by 6 )

x = 7

Thus width = 7 cm and length = 7 + 8 = 15 cm

The figure is made of 4 rectangles, thus

area = 4 × (7 × 15) = 4 ×105 = 420 cm²

Answer:

278.25 cm2

Step-by-step explanation:

If the width of the rectangle is x (cm), as the length is 8cm longer, so that the length of the rectangle is: x + 8 (cm).

In the attached image, we can see the length of each side. Total length of the sides are 90 cm.

=> (x + x + 8) + x + 8 + (x+8) + (x + x + 8) + x + 8 + (x +8) = 90

=> 8x + 48 = 90

=> 8x = 90 - 48 = 42

=> x =42/8 = 5.25 (cm)

=> The width of the rectangle is 5.25cm

=> The length of the rectangle is: 5.25 + 8 = 13.25 cm

=> The area of one rectangle is: Length x Width = 5.25 x 13.25 = 69.5625 cm2

As the 8-sided shape is made from 4 rectangles, so that:

Area of 8 sided shape = 4 x Area of the rectangle = 4 x 69.5625 = 278.25 cm2

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