Alternate-vertices-of-a-regular-hexagon-are-joined-as-shown-What-fraction-of-the-total-area-of-the-hexagon-is-shaded-Justify-your-answer-

Question Number 16756 by Tinkutara last updated on 26/Jun/17

Alternate vertices of a regular hexagon

are joined as shown . What fraction of

the total area of the hexagon is

shaded ? (Justify your answer .)

Commented by Tinkutara last updated on 26/Jun/17

Answered by mrW1 last updated on 26/Jun/17

\frac{Side small}{Side large} = \frac{2}{2 \sqrt{3}} = \frac{1}{\sqrt{3}}

\frac{Area small}{Area large} = {(\frac{Side small}{Side large})}^{2} = {(\frac{1}{\sqrt{3}})}^{2} = \frac{1}{3}

Answered by RasheedSoomro last updated on 26/Jun/17

Commented by RasheedSoomro last updated on 26/Jun/17

AnOther way

\frac{Small triangles in inner hexagon}{Small triangles in outer hexagon} = \frac{12}{36} = \frac{1}{3}

Commented by Tinkutara last updated on 26/Jun/17

Thanks Sir!