Waste less time on Facebook — follow Brilliant.
×

This is a geometry problem which I seem is tough. See if you can solve it and give me the proper explanation and answer as I am studying for NECM level-II exam. Please give me as fast as possible.

Sides of PQRS touch a circle of 8cm diameter, as shown in the figure. Find the area of PQRS if its perimeter is 52cm.

Note by Ashwin Korade
3 years ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

The area of quadrilateral \(PQRS\) is \(104\) cm\(^2\).
Let the bases of the four triangles \(\triangle OPQ\), \(\triangle OQR\), \(\triangle ORS\) and \(\triangle OSP\), \(PQ, QR, RS\) and \(SP\), be \(a, b, c\) and \(d\) respectively. Since all the bases are tangential to the circles, this means that the heights \(h\) of the four triangles are equal to the radius of the circle which is \(4\) cm. Therefore the area \(A\) of the quadrilateral \(PQRS\):

\(A = \frac {1}{2} (a+b+c+d) h = \frac {1}{2} \times\) perimeter \(\times\) radius \(= \frac {1}{2} \times 52 \times 4 = \boxed{104} \) cm\(^2\).

Chew-Seong Cheong - 3 years ago

Log in to reply

It is 104 because radius is 4 cm. Rest I too did the same.

Kartik Sharma - 3 years ago

Log in to reply

Sorry, I got the radius wrong. It should be 4 cm and hence the area should be 104 \(cm^2\).

Chew-Seong Cheong - 3 years ago

Log in to reply

FYI - You can edit your comment directly by clicking on the pencil on the right (it's to the left of the time stamp).

Calvin Lin Staff - 3 years ago

Log in to reply

104 cm2 as i can see!

Shraman Das - 3 years ago

Log in to reply

since PQ + QR + RS + SP =52 & area of the quadrilateral is equal to area of four triangles named ( if O is the center of the circle) [ORQ] + [OQP] +[OSP] + [ORS]. and height of four triangles is equal to the radius of the circle= 4 cm so the area is 1/24(PQ + QR + RS + SP)=1/2452=104 sq cm

Nibedan Mukherjee - 3 years ago

Log in to reply

I got 104

Krishna Sharma - 3 years ago

Log in to reply

answer is 104 cm^2 if the diagonals of the quadrilateral meet at center of the circle.

Aditya Vikram - 3 years ago

Log in to reply

That assumption isn't necessary.

Calvin Lin Staff - 3 years ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...