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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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