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.

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

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )