In quadrilateral ABCD, M is the mid-point of AC. If area (BCDM) is 20 $c m^{2}$ , then find the area (ABMD). [3 MARKS]

Open in App

Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

BM is the median of $△$ ABC

ar( $△$ ABM) = ar( $△$ BMC)------(1)

DM is the median of $△$ ADC

Similarly, ar( $△$ AMD) = ar( $△$ MCD)------(2)

Adding (1) and (2) ,

ar(ABMD) = ar(BCDM) = 20 $c m^{2}$

Suggest Corrections

Similar questions

In a quadrilateral ABCD AB = 6 cm, BC = 8 cm, CD = 8 cm and AC=10cm.The area of the quadrilateral is 60.67 cm². Find DA.
[4 MARKS]

ABCD is a parallelogram and E and F are mid-points of AD and BC respectively. P is any point on AB. If area of ΔEDF=16 $c m^{2}$ , then find the area of ( ΔAEP+ ΔBFP) [3 MARKS]

Q. In a quadrilateral ABCD, M is the midpoint of AC. Prove that

ar (A B M D) = ar (D M B C)

A B C D

is a quadrilateral

A C = 19 c m

. The lengths of perpendiculars from

B

and

D

A C

are

5 c m

and

7 c m

respectively. Then, the area of

A B C D

(in

c m^{2})

is:

Q. In the given figure, if AC = 8 cm, DQ = 4 cm, and BP = 6 cm, find the area (cm

^{2}

) of the quadrilateral ABCD.

Join BYJU'S Learning Program

In quadrilateral ABCD, M is the mid-point of AC. If area (BCDM) is 20 cm2, then find the area (ABMD). [3 MARKS]

Concept : 1 Mark Application : 1 Mark Calculation : 1 Mark BM is the median of △ABC ar(△ABM) = ar(△BMC)------(1) DM is the median of △ADC Similarly, ar(△AMD) = ar(△MCD)------(2) Adding (1) and (2) , ar(ABMD) = ar(BCDM) = 20 cm2

In quadrilateral ABCD, M is the mid-point of AC. If area (BCDM) is 20 $c m^{2}$ , then find the area (ABMD). [3 MARKS]

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

BM is the median of $△$ ABC

ar( $△$ ABM) = ar( $△$ BMC)------(1)

DM is the median of $△$ ADC

Similarly, ar( $△$ AMD) = ar( $△$ MCD)------(2)

Adding (1) and (2) ,

ar(ABMD) = ar(BCDM) = 20 $c m^{2}$