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Question
In the given figure, ΔABC is an equilateral triangle the length of whose side is equal to 10 cm, and ΔADC is right-angled at D and BD= 8cm. Find the area of the shaded region.
Solution
Given:
Side if equilateral triangle ABC=10 cm
= 8 BD cm
Area of equilateral `Δ ABC=sqrt3/4 a^2` (where a=10 cm )
Area of equilateral `Δ ABC=sqrt3/4xx10^2`
=`25sqrt3`
=`25xx1.732`
=`43.30 cm^2`
In the right , ΔBDC we have:
`BC^2=BD^2+CD^2`
⇒`10^2=8^2+CD^2`
⇒`CD^2=10^2-8^2`
⇒`CD^2=36`
⇒`CD=6`
Area of triangle` ΔBCD=1/2xxbxxh`
=`1/2xx8xx6`
=`24 cm^2`
Area of the shaded region=`"Area of ΔABC- Area of ΔBDC"`
=`43.30-24`
=`19.3 cm^2`
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