Find the area of a whose sides are 6cm, 8cm, 12cm respectively,
Answers
Answer:
ok..but wjat is the shape of that
Answer:
247
Step-by-step explanation:
Given ABCD is a quadrilateral having sides AB=6cm, BC=8cm, CD=12cm and DA=14 cm. Now. Join AC.
We have, ABC is a right angled triangle at B.
Now, AC2=AB2+BC2 [by Pythagoras theorem]
=62+82=36+64=100
⇒ AC=10cm [taking positive square root]
∴Area of quadrilateral ABCD=Area of △ABC+Area of △ACD
Now, area of △ABC=12×AB×BC [∵area of triangle=12(base×height)]
=12×6×8=24cm2
In △ACD, AC=a=10cm,CD=b=12cm
and DA=c=14cm
Now,semi-perimeter of △ACD,s=a+b+c2=10+12+142=362=18cm
Area of △ACD=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√ [by Heron's formula]
=18(18−10)(18−12)(18−14)−−−−−−−−−−−−−−−−−−−−−−−−√
=18×8×6×4−−−−−−−−−−−−√=(3)2×2×4×2×3×2×4−−−−−−−−−−−−−−−−−−−−−−√
=3×4×23–√×2=246–√cm2
From Eq. (i)
Area of quadrilateralABCD=Area of △ABC+Area of △ACD
=24+246–√=24(1+6–√)cm2
Hence, the area of quadrilateral is 241+6–√−−−−−−√cm2.