Question

find the area of each shaded region.Assume all angles that appear to be right angles are right angles.(pls. take this seriusly i need help...pls. answer all of this)​

Answer 1

Solution 1) :-

→ Outer breadth = 7ft

→ Inner breadth = 3 ft .

Let width of path is x ft .

so,

→ Inner breadth = Outer breadth - 2x

→ 3 = 7 - 2x

→ 2x = 7 - 3

→ 2x = 4

→ x = 2 .

then,

→ Inner Length = Outer Length - 2x = 12 - 2 * 2 = 12 - 4 = 8 ft .

therefore,

→ Shaded area = Outer rectangle area - Inner rectangle area = 7 * 12 - 3 * 8 = 84 - 24 = 60 ft² (Ans.)

Solution 2) :- (Refer to image for all dimensions.)

→ Shaded area = Area of rectangle - Area of square

→ Shaded area = L * B - (side)²

→ Shaded area = 12 * 8 - 4²

→ Shaded area = 96 - 16

→ Shaded area = 80 cm² (Ans.)

Solution 3) :-

→ Shaded area = Area of rectangle - Area of ∆

→ Shaded area = L * B - (1/2) * Base * Height

→ Shaded area = 16 * 12 - (1/2) * 14 * 12

→ Shaded area = 192 - 84

→ Shaded area = 108 cm² (Ans.)

Solution 4) :- (Refer to image for all dimensions.)

→ Shaded area = Area of ∆ - Area of rectangle

→ Shaded area = (1/2) * Base * Height - L * B

→ Shaded area = (1/2) * 6 * 7 - 4 * 2

→ Shaded area = 21 - 8

→ Shaded area = 13 m² (Ans.)

Solution 5) :-

→ Shaded area = Outer circle area - Inner circle area

→ Shaded area = πR² - πr² = π(R² - r²) = π(R + r)(R - r)

→ Shaded area = π(14 + 7)(14 - 7)

→ Shaded area = (22/7) * 21 * 7

→ Shaded area = 22 * 21

→ Shaded area = 462 cm² (Ans.)

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