Question

find the area of a quadrilateral ABCD in which a b is equal to 3 cm BC is equal to 4 cm CD is equal to force and the age girl 25 cm and ac is equal to 5 centimetre​

Answer 1

Answer :

The area of Quadrilateral ABCD is 15.2cm sq.

Step-by-step explanation :

Correct Question :

Find the area of a quadrilateral ABCD in which AB is equal to 3 cm,BC is equal to 4 cm, CD is equal to 4 cm, is equal to 5 cm, and AC is equal to 5 cm.

Solution :

Given that :

• AB is equal to 3 cm.
• BC is equal to 4 cm.
• CD is equal to 4 cm.
• AC is equal to 5 cm.

To Find :

The area of a quadrilateral.

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Area of Quadrilateral :

Area of ∆ABC + Area of ∆AD.

To Find :

Area of ∆ ABC

We know that  :

By Heron's formula :

$\sf \implies \sqrt{s(s - a)(s - b)(s - c}\\\\ \implies s = \dfrac{a + b + c}{2}=\dfrac{3 + 4 + 5}{2} = \dfrac{12}{2}\\\\ \implies 6\\\\ \textbf{\underline{\underline{Area of triangle}}} :\\\\ \implies \sqrt{s(s - a)(s - b)(s - c)}\\\\ \implies \sqrt{6(6 - 3)(6 - 4)(6 - 5)}{cm}^{2}\\\\ \implies \sqrt{6 \times 3 \times 2 \times 1}{cm}^{2}\\\\ \implies\sqrt{6 \times 6}  = 6 {cm}^{2}$

To Find :

Area of ∆ ADC.

By Heron's formula :

$\implies \sf s=\dfrac{a + b + c}{2}\\\\ \implies \dfrac{5 + 4 + 5}{2} = \dfrac{14}{2} = 7\\\\  \\ \textbf{\underline{\underline{Area \: of \: triangle :-}}}\\\\ \implies \sqrt{s(s - a)(s - b)(s - c)}\\\\ \imp\implies 2 \sqrt{21}{cm}^{2}\\\\ \implies 2 \times 4.58\\\\ \implies 9.16 {cm}^{2}$

As we know :

Area of ∆ABC + Area of ∆AD.

We have,

Area of ∆ ABC  = 6cm²

Area of ∆ ADC = 9.16 cm²

Put values :

$\sf \implies ( 6 + 9.16) {cm}^{2}\\\\\implies 15.16 {cm}^{2}\\\\ \implies 15.2 {cm}^{2}\\\\\\\bigstar\;\textbf{\underline{\underline{Hence,The area of Quadrilateral ABCD is 15.2cm sq.}}}$

$\bigstar\; \textbf{\underline{Refer the attachment for the figure.}}}$