Question

1.
Find the area of the shaded region in the
following figures
​

Answer 1

Answer:

a) 91 m²

b.) 125 m²

c.) 24 m²

Explanation:

a.) To find this shaded area, we have to subtract the area of the smaller square from the area of the bigger square.

Bigger square side = 10 m

Smaller square side = 3 m

∴ Shaded area = Area of bigger square - Area of smaller square

=> 10² - 3²         (Area of square = a² where a is square's side)

=> 100 - 9 => 91 m²

b.) All smaller squares are congruent.

Shaded area = Area of bigger square - 4(Area of smaller square)

Bigger square's side = 15 m

Smaller square's side = (15 - 5)/2 = 10/2 => 5 m      (All smaller squares are congruent. Thus, the side left after subtracting 5 from 15 is divided equally into both squares.)

∴ Shaded area = Area of bigger square - 4(Area of smaller square)

=> 15² - 4(5²)

=> 225 - 4(25) => 225 - 100 => 125 m²    (You can also use identity a² - b² to subtract them)

c.) All smaller rectangles are congruent.

Shaded area = Area of bigger rectangle - 4(Area of smaller rectangles)

Bigger rectangle's length and breadth = 25 m and 10 m

Smaller rectangle's length = (25 - 4)/2 = 21/2 => 10.5 m

Smaller rectangle's breadth = (10 - 4)/2 = 6/2 => 3 m

∴ Shaded area = Area of bigger rectangle - 4(Area of smaller rectangle)

=> 15(10) - 4[10.5(3)]      (Area of rectangle = lb where l = length and b = breadth of the rectangle)

=> 150 - 126 => 24 m²

Answer 2

Answer:

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