Question

The triangles insides the equilateral triangles are also equilateral and embossed . If side of each interior embossed equilateral triangle is 5 cm , the unembossed area is

Answer 1

Answer:

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Answer 2

Given,

Each side of hexagon = 6 cm ( take reference from subpart 9-(i) )

Each side of embossed triangle = 5 cm

Solution,

For calculating the area equilateral triangle use following formula,

Area$\[ = \frac{{\sqrt 3 }}{4}{a^2}\]$ ( where 'a' is the side of the equilateral triangle)

Hence,

Unembossed area = Area of hexagon - 6 × area of embossed triangles

                               $\[\begin{array}{l} = 6 \times \frac{{\sqrt 3 }}{4} \times {6^2} - 6 \times \frac{{\sqrt 3 }}{4} \times {5^2}\\ = 6 \times \frac{{\sqrt 3 }}{4} \times \left( {36 - 25} \right)\\ = \frac{{33\sqrt 3 }}{2}\;{\rm{c}}{{\rm{m}}^2}\end{array}\]$

Hence,  the unembossed area is $\[\frac{{33\sqrt 3 }}{2}\;{\rm{c}}{{\rm{m}}^2}\]$.