In the given figure, $A B C D$ is a rectangle, where $A B = 8$ cm, $B C = 6$ cm and the diagonals bisect each other at $O$ . Find the area of the shaded region by Heron's formula.

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Solution

Given : $A B = 8 c m$ $B C = 6 c m$

$A C = \sqrt{8^{2} + 6^{2}} = 10$

$A O = \frac{10}{2} = 5$

$S = \frac{5 + 5 + 8}{2} = 9$

Area of $Δ A O B = \sqrt{S (S - a) (S - b) (S - c)} = \sqrt{9 (9 - 8) (9 - 5) (9 - 5)} = \sqrt{9 \times 1 \times 4 \times 4} = 3 \times 4$

Area of $Δ A O B = 12$ sq. units.

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In the given figure, ABCD is a rectangle, where AB=8 cm, BC=6 cm and the diagonals bisect each other at O. Find the area of the shaded region by Heron's formula.

Given : AB=8cm BC=6cmAC=√82+62=10 AO=102=5 S=5+5+82=9Area of ΔAOB=√S(S−a)(S−b)(S−c)=√9(9−8)(9−5)(9−5)=√9×1×4×4=3×4 Area of ΔAOB=12 sq. units.

In the given figure, $A B C D$ is a rectangle, where $A B = 8$ cm, $B C = 6$ cm and the diagonals bisect each other at $O$ . Find the area of the shaded region by Heron's formula.