Q. 23.9( 17 Votes )

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Answer :

We know, area of rectangle = length × breadth

(i) Area of colored region(green) = area of outer rectangle – area of inner rectangle

Now, dimensions of outer rectangle = 12 × 8

⇒ area of outer rectangle = 96 m^{2}

Width of each strip = 4 m

Therefore, dimension of inner rectangle = (12 – 3) × (8 – 3)

⇒ area of inner rectangle = 45 m^{2}

⇒ area of colored region = 96 – 45 = 51 m^{2}

(ii) Area of colored region = area of whole rectangle – area of 4 small rectangles

Now, dimensions of whole rectangle = 26 × 14

⇒ area of outer rectangle = 364 m^{2}

Width of each strip = 3 m

Let length of rectangle be ‘l’ and width be ‘b’

Now,

Length of 2 small rectangles + width of strip = 26 m

⇒ 2l + 3 = 26

⇒

breadth of 2 small rectangles + width of strip = 14 m

⇒ 2b + 3 = 14

⇒

⇒ area of one small rectangle = lb

⇒ area of four small rectangles = 231 m^{2}

⇒ area of colored region = 364 – 231 = 133 m^{2}

(iii) Area of colored region(violet) = area of outer rectangle – area of inner rectangle

Now, dimensions of inner rectangle = 16 × 9

⇒ area of outer rectangle = 144 m^{2}

Width of each strip = 4 m

Therefore, dimension of outer rectangle = (16 + 2(4)) × (9 + 2(4)) = 24 × 17

⇒ area of inner rectangle = 408 m^{2}

⇒ area of colored region = 408 – 144 = 264 m^{2}

(iv) Area of colored region(orange) = area of outer rectangle – area of inner rectangle

Now, dimensions of outer rectangle = 28 × 20

⇒ area of outer rectangle = 560 m^{2}

Width of each strip = 3 m

Therefore, dimension of outer rectangle = (28 - 2(3)) × (20 - 2(3)) = 22 × 14

⇒ area of inner rectangle = 308 m^{2}

⇒ area of colored region = 560 – 308 = 252 m^{2}

(v)

Area of colored region = area of strip I + 4 × area of strip II

Now, dimension of strip I = 3 cm × 120 cm

Hence, area of strip I = 360 cm^{2}

Now, width of strip II = 3 cm

Also, 2 × length of strip II + width of strip I = 90 cm

⇒ 2 × length of strip II + 3 = 90

⇒ length of strip II = 43.5 cm

Hence, area of II strip = 43.5 × 3 = 130.5 cm^{2}

Hence, area of required region = 360 + 4(130.5) = 882 cm^{2}

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