Question

5. Calculate the area of quadrilateral ABCD in which :
AB = 24 cm, AD = 32 cm, BAD = 90°,
and BC = CD = 52 cm.
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Answer 1

Step-by-step explanation:

first let's find out the diagonal

in ∆ adb

db^2= da^2+ab^2

db^2= (32cm)^2+(24cm)^2

db=√1024cm^2+√576cm^2

db=√1600

db =40cm

now area of the ∆dab=1/2*base*altitude

=1/2*24cm*32cm

=384cm^²

area of the ∆dbc, using herons formula

let dc, cb and db be x, y and z

s= x+y+z/2= 52+52+40/2=144/2=72

area of the ∆dbc= √s(s-x)(s-y)(s-z)

=√72(72-52)(72-52)(72-40)

=√72*20*20*32

=√921600

=960cm^2

therefore, area of the quadrilateral= area of the ∆dab +area of the ∆dbc

ar. of the quadrilateral abcd= 384cm^2+ 960cm^2

=1344 cm^2

hope this help

Answer 2

Answer:

Step-by-step explanation: