Let $P$ be an interior point of a convex quadrilateral $A B C D$ and $K, L, M, N$ be the midpoints of $A B, B C, C D, D A$ respectively. If $area (P K A N) = 25, area (P L B K) = 36, area (P M D N) = 41,$ then $area (P L C M) =$ is

20

No worries! We‘ve got your back. Try BYJU‘S free classes today!

29

No worries! We‘ve got your back. Try BYJU‘S free classes today!

52

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

54

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $52$
From the given data,

Area of $Δ A P N =$ Area of $Δ D P N$ (As the base length is same, $A N = D N$ and the perpendicular from $P$ to the both bases is same)

So,
$p + q = 25 q + r = 36 p + s = 41 s + r = (?)$

$\Rightarrow s + r = p + s + q + r - p - q = 41 + 36 - 25 = 52$

Suggest Corrections

Similar questions

Q. In a rectangle

A B C D

P

Q

R

and

S

are the midpoints of the sides

A B

B C

C D

and

D A

respectively. Find the area of

P Q R S

in terms of area of

A B C D

Q. E,F,G,H are respectively, the midpoints of the sides AB,BC,CD and DA of parallelogram. ABCD. Show that the quadrilateral EFGH is a parallelogram and that its area is half the area of the parallelogram ABCD.

In the given figure, $A B C D$ is a rectangle in which $A B = 40 c m$ and $B C = 25 c m$ . If P,Q,R.S be the midpoints of AB, BC, CD and DA respectively, find the area of the shaded region.

Let ABCD be a parallelogram of area $124 c m^{2}$ If E and F are the midpoints of sides AB and CD respectively, then find the area of parallelogram AEFD.

In a rectangle ABCD, P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively and T is the point on RS such that RT = 2TS. If the area of ABCD is 'k' times the area of ∆PQT then 'k' is

Join BYJU'S Learning Program

Let P be an interior point of a convex quadrilateral ABCD and K,L,M,N be the midpoints of AB,BC,CD,DA respectively. If area(PKAN)=25,area(PLBK)=36,area(PMDN)=41, then area(PLCM)= is

The correct option is C 52From the given data, Area of ΔAPN=Area of ΔDPN (As the base length is same, AN=DN and the perpendicular from P to the both bases is same) So, p+q=25q+r=36p+s=41s+r=(?) ⇒s+r=p+s+q+r−p−q=41+36−25=52

Let $P$ be an interior point of a convex quadrilateral $A B C D$ and $K, L, M, N$ be the midpoints of $A B, B C, C D, D A$ respectively. If $area (P K A N) = 25, area (P L B K) = 36, area (P M D N) = 41,$ then $area (P L C M) =$ is