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. 

 

 

Answer 1

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`