Math, asked by malarrajan53, 5 months ago

find the area of quadrilateral ABCD, whose sides are AB=8cm, BC=15cm, CD=12cm,AD=25cm and angleB =90°. Please guys step by step explanation ​

Answers

Answered by Flaunt
14

\huge\bold{\gray{\sf{Answer:}}}

Explanation:

Given :

Sides of Quadrilateral ABCD

AB=8cm;BC=15cm;CD=12cm and AD=25cm

∠B=90°

To Find:

Area of quadrilateral ABCD

In ∆ABC

 {AC}^{2}  =  {AB}^{2}  +  {BC}^{2}

 =  >  {AC}^{2}  =  {8}^{2}  +  {15}^{2}

 =  >  {AC}^{2}  = 64 + 225 = 289

AC =  \sqrt{289}  = 17cm

Formula:

\bold{\boxed{Area \: of \: triangle =  \frac{1}{2} \times base \times height}}

Area \: of \:∆ ABC=  \frac{1}{2}  \times 15 \times 8 = 60 {cm}^{2}

IN ∆ACD

AD=25cm;AC=17cm and CD=12cm

S =  \frac{a + b + c}{2}  =  \frac{25 + 17 + 12}{2}  =  \frac{54}{2}  = 27

\bold{\orange{S=27}}

Area of∆ ACD=

 \sqrt{S(s- a)(s- b)(s - c)}

 =  >  \sqrt{27(27  - 17)(27 - 12)27 - 25)}

 =  >  \sqrt{27 \times 10 \times 15 \times 2}

 =  \sqrt{3 \times 3 \times 3 \times 2 \times 5 \times 3 \times 5 \times 2}

 = 3 \times 3 \times 2 \times 5 = 90 {cm}^{2}

Area of ∆ACD =90 {cm}^{2}

Now,\bold{Area \:of \:ABCD} =\bold{\pink{∆ABC+∆ACD}}

 = 60 {cm}^{2}  + 90 {cm}^{2}

 \bold{\red{= 150 {cm}^{2}}}

Attachments:
Answered by minasharmaminaedu
0

CONCEPT

USING AREA OF TRIANGLE

PYTHAGORAS THEOREM

HERONS FORMULA

GIVEN

AB=8CM

BC=15CM

CD=12CM

AD=25CM

ANGLE B = 90°

FIND

AREA OF QUADRILATERAL

SOLUTION

AREA OF  TRIANGLE ABC = 1/2× BASE × HEIGHT

1/2×8×15

60CM²

NOW USING PYTHAGORAS THEREOM

AC²=AB²+BC²

AC²=8²+15²

AC²=64+225

AC²=289

AC=17CM

AB=8CM

BC=15CM

BY HERONS FORMULA

S=(A+B+C)/2

S=17+8+15/2

S=32.5 CM

AREA OF TRIANGLE ADC= √32.5(32.5- 17) × 32.5(32.5-8) × 32.5(32.5- 15)

AREA OF TRIANGLE ADC = √503.75×796.25×568.75

AREA OF TRIANGLE ADC = 15104.03 CM²

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