In the given figure, ABC is an equilateral triangle the length of each side is equal to 10 cm, and DBC is right angled triangle at D and BD=8 cm. Find the area of the shaded region.

Question

In the given figure, ABC is an equilateral triangle the length of
each side is equal to 10 cm, and DBC is right angled triangle at D
and BD=8 cm Find the area of the shaded region

Lovina Kansal · Accepted Answer

Dear student
Area of equilateral triangle ABC=34102cm2=253cm2Now,In triangle BDCBy Pythagoras TheoremBC2=BD2+DC2DC2=102-82DC2=36DC=6cm Therefore, Area of triangle BDC=12×DC×BD=12×6×8=24cm2Hence,Area of shaded region=Area of △ABC -Area of △BDC=253-24cm2
Regards