Question

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

Answer 1

Given:

Side if equilateral triangle ABC = 10 cm

BD = 8 cm

In the right \(\triangle BDC\), we have:

BC² = BD² + CD²

\(\Rightarrow\) 10² = 8² + CD²

\(\Rightarrow\) CD² = 10² - 8²

\(\Rightarrow\) CD² = 36

\(\Rightarrow\) CD = 6

Area of triangle \(\triangle BCD =\frac{1}{2}\times b \times h\)

= \(\frac{1}{2}\times 8\times 6\)

= 24 cm²

Area of the shaded region = Area of \(\triangle ABC\) - Area of \(\triangle BDC\)

= 43.30 -24

= 19.3 cm²