Answer:
Area of shaded rectangle = 42 cm²
55%
Step-by-step explanation:
The length of the shaded area is equal to the length of the white rectangle.
Therefore, length of shaded rectangle = 7 cm
The width of the shaded rectangle is equal to the length of the white rectangle <u>minus</u> two widths of the white rectangle.
Therefore, width = 7 - (2 x 0.5) = 6 cm
Area of shaded rectangle = width x length
= 6 x 7
= 42 cm²
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Perimeter of a square = 4 × side length
If the perimeter of the square is 40 cm,
then the side length = 40 ÷ 4 = 10 cm
Area of a square = side length x side length
⇒ area of this square = 10 x 10 = 100 cm²
To determine the shaded area, calculate the areas of the 2 white triangles and subtract these from the area of the square.
Area of a triangle = 1/2 x base x height
⇒ area of left triangle = 1/2 x (10 - 7) x 10 = 15 cm²
⇒ area of right triangle = 1/2 x 10 x (10 - 4) = 30 cm²
Therefore, shaded area = 100 - 15 - 30 = 55 cm²
To calculate the percentage, divide the shaded area by the area of the square and multiply by 100:
(55 ÷ 100) × 100% = 55%
