Question

12. A long time ago Dulani found an island shaped like a triangle with three
straight shores of length 3 km, 4 km and 5 km. He said nobody could come
within 1 km of his shore. What was the area of his exclusion zone?​

Answer 1

Given :- A long time ago Dulani found an island shaped like a triangle with three straight shores of length 3 km, 4 km and 5 km. He said nobody could come within 1 km of his shore. What was the area of his exclusion zone ?

Solution :-

we know that, 3,4,5 forms a right angled ∆ .

it has been said that, nobody could comewithin 1 km of his shore.

we can say that, The exclusion zone can be made up of 6 pieces.

• Three are rectangular pieces, each 1 km wide and with lengths 3km, 4km, and 5 km.
• The other three pieces are sectors of circles of radius 1 km.

we know that,

• Area of rectangle = Length * Breadth.
• Area of circle = π * (radius)² .

then,

→ Area of exclusion zone = Area of three rectangular pieces + Area of circle = 3 * 1 + 4 * 1 + 5 * 1 + π(1)² = 3 + 4 + 5 + π = 12 + 3.14 = (15.14) km² .

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