Cyclic quadrilateral

Geometry Level 2

Find the area of a cyclic quadrilateral with sides 2, 2, 3, 1.

Round your answer to the nearest hundredth.


The answer is 3.46.

View wiki
Hamza A by Hamza A , 19, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

By the Brahmagupta's Fomula , we have

A = ( s − a ) ( s − b ) ( s − c ) ( s − d ) A=\sqrt{(s-a)(s-b)(s-c)(s-d)}

s = 2 + 2 + 3 + 1 2 = 4 s=\dfrac{2+2+3+1}{2}=4

A = ( 4 − 2 ) ( 4 − 2 ) ( 4 − 3 ) ( 4 − 1 ) = 12 ≈ = A=\sqrt{(4-2)(4-2)(4-3)(4-1)}=\sqrt{12} \approx= 3.46 \large \boxed{3.46}

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Hamza A
Jan 18, 2016

by brahmagupta`s formula we have

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Jan 19, 2016

we could use A = (abcd)^0.50

1 Helpful 0 Interesting 0 Brilliant 0 Confused

i don`t think that this works for all cyclic quadrilaterals

do you know in which cases it works?

Hamza A - 5 years, 4 months ago

Log in to reply

It works for bicentric quadrilaterals.

Anupam Nayak - 5 years, 4 months ago

Log in to reply

interesting ,thanks for telling me about it

Hamza A - 5 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...