Question

Find The Area Of The Shaded Region.​

Answer 1

Area of shaded region = Area of ∆ - Area of sq.

Area of ∆ with herons formula ;

$\pink{ \bf \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ \\ \sf= \sqrt{6(6 - 4)(6 - 4)(6 - 4)} \\ \\ = \sf \sqrt{6 \times 2 \times 2 \times 2 } \\ \\ \sf \: \green{ = 4 \sqrt{3} \: \: {cm}^{2} } \\ \\ \\ \\ \sf \: Area \: \: of \: \: square = a² \\ \\ \sf \: Area \: \: of \: \: sq. = 1cm²$

$\small\sf Now \: \: Area \: \: of \: \: shaded \: \: region ; \\ \\ = \sf 4 \sqrt{3} {cm}^{2} - 1 {cm}^{2} \\ \\ \boxed{\purple{\bf \sqrt{3} = 1.7}} \\ \\ = \sf \: 4 \times 1.7 - 1 \\ \\ \sf \: = 6.8 - 1 \\ = \boxed{\boxed{\boxed{\red{ \sf \: 5.8 {cm}^{2} }}}}$

I HOPE IT HELPS.