Math, asked by kanishksaboo9, 2 months ago

the sides of quadrilateral, taken in order are 5,12,14 and 15 meters respectively and the angle contained by the first two sides is a right angle. find it's area​

Answers

Answered by itscandycrush
18

Given:-

  • Sides of quadrilateral are 5, 12, 14 and 15 m.
  • The angle contained by the first two sides is a right angle.

════◄••❀••►════

To Find:-

  • Area of the quadrilateral

════◄••❀••►════

Formula Used:-

  • Area of right angle triangle = ½ × Base × Height
  • Area of triangle = By Heron's Formula
  • Pythagorean theorem = h² = p² + b²

════◄••❀••►════

Solution:-

➥ Let the quadrilateral be ABCD.

Here;

AB = 5m

BC = 12m

CD = 14m

DA = 15m

════◄••❀••►════

➥ Area of ∆ABC

= ½ × Base × Height

= ½ × BC × AB

= ½ × 12 × 5

= 60 ÷ 2

= 30m²

════◄••❀••►════

Now,

➥ By Pythagorean Theorem

(AC)² = (BC)² + (AB)²

(AC)² = (12)² + (5)²

(AC)² = 144 + 25

AC = 169

AC = 13m.

════◄••❀••►════

➥ For Area of ∆ADC

Value of s

½(AD + AC + CD)

= ½(15 + 13 + 14)

= ½ × 42

= 42 ÷ 2

= 21m

➥ Area of ∆ADC by Heron's Formula

= s(s - AD)(s - AC)(s - CD)

= 21(21 - 15)(21 - 13)(21 - 14)

= 21 × 6 × 8 × 7

= 7 × 3 × 3 × 2 × 2 × 2 × 2 × 7

= 7 × 3 × 2 × 2

= 21 × 4

= 82m²

════◄••❀••►════

➥ Area of quadrilateral ABCD

= Area of ∆ABC + Area of ∆ADC

= 30 + 82

= 112m²

════◄••❀••►════

Answer:-

Area of quadrilateral is 112m²

════◄••❀••►════

Attachments:
Answered by rajatraj929
1

Answer:

Given that sides of quadrilateral are AB = 5 m, BC = 12 m, CD = 14 m and DA = 15 m AB = 5m, BC = 12m, CD = 14 m and DA = 15 m Join AC In ∆ABC By applying Pythagoras theorem. By using Heron’s formula Area of quadrilateral ABCD = area of ( ∆ABC) + Area of (∆ADC) = 30+84 = 114 m2Read more on Sarthaks.com - https://www.sarthaks.com/110477/the-sides-of-a-quadrilateral-taken-in-order-are-5-12-14-and-15-meters-respectively

Similar questions