Question

AB//DC and DA is perpendicular to AB . Further, DC =7cm ,CB=10cm and AB=13cm. Find the area of the quadrilateral ABCD

Answer 1

Answer:

80 cm²

Step-by-step explanation:

GIVEN:-

AB║DC

DA⊥AB

DC =7 cm

CB=10 cm  

AB=13 cm

TO FIND:-

area of the quadrilateral ABCD

SOLUTION:-

Draw CM⊥AB

∴AM=DC=7 cm

MB=AB-AM

=13-7

=6 cm

∴In rt. ∠d ΔCMB,

CM²=10²-6²

      =(10+6)(10-6)

      =16*4

CM² =64

CM=√64=8 cm

∴Ar(ABCD)=Area of Trapezium

=1/2×height×sum of parallel sides

=1/2×8×(13+7)

=4*20

=80 cm²

Answer 2

Area of parallelogram + Area of triangle

Area of ABCD =area of triangle +area of parallelogram

Area of parallelogram =l×b=10×7=70cm sq

Area of triangle =1/2×b×h

Use Pythagorean theorem

A sq=B sq+P sq

10 sq=B sq+6 sq

100-36=B sq

8=B

So, area of triangle =1/2×6×8=24cm sq

Area of whole figure =24 +70 =94cm sq