Question

All the triangles shown in the adjacent figure are equilateral. If the length if the side of the two largest triangles is 3cm, then the area of the shaded region (in cm^2): ​

Answer 1

Answer:

VIQ BTW THIS QNA ANSWER IS 3/8 OPT:- D

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Answer 2

Area of the shaded region is 0.65 $cm^{2}$

Given,

All the triangles are equilateral triangles _________ (i)

and,

Length of one of the sides of the largest triangle is 3 cm _______ (ii)

Solution steps-

If length of one side is 3 cm, then the length of all the sides of both the largest triangles are 3 cm.

By (ii), the sides of the smaller triangles are 1 cm each

Now to find the area of shaded region (i.e., 2) we have to find the area of triangle 123 and subtract it by the area of triangle 1, then we will half the obtained area to get the desired solution.

Area of an equilateral triangle is $(\sqrt{3} /4)a^{2}$

where a is the sides of the triangle

Now, since the length of each side of triangle 123 is 2 cm, hence,

Area of 123 = $(\sqrt{3} /4)*2^{2}$

                   ≈ 1.73205            ____________ (iii)

Area of 1 = $(\sqrt{3} /4)*1^{2}$

                   ≈ 0.43301            ____________ (iv)

Subtracting (iv) from (iii)

1.73205 - 0.43301 = 1.30      ____________ (v)

Dividing (v) by 2 to get the required area

1.30/2 = 0.65

Hence, the area of the shaded region is 0.65 $cm^{2}$.