Question

In quadrilateral ABCD, BC is the diagonal, DO is perpendicular to BC, and CX is perpendicular to AB. If AB = 25 cm, BC = 16 cm, CX =8 cm, and DO = 5 cm, find the area of the quadrilateral. ​

Answer 1

Answer:

The area of quadrilateral ABCD=140 square cm

Step-by-step explanation:

BC=16 cm

AB=25 cm

CX=8 cm

OD=5 cm

Area of triangle=

Using the formula

Area of triangle ABC=

Area of triangle BCD=

Area of quadrilateral ABCD=Ar(ABC)+ar(BCD)=100+40=140 square cm

Hence, the area of quadrilateral ABCD=140 square cm

Step-by-step explanation:

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Answer 2

Given:

1. AB = 25 cm, BC = 16 cm, CX =8 cm, and DO = 5 cm

2. DO is perpendicular to BC, and CX is perpendicular to AB

Step-by-step explanation:

Divide the quadrilateral in 2 triangle,

First, In ΔABC

Base = AB = 25cm , Height = CX = 8cm

Area of ΔABC  $= \frac{1}{2}*b*h$

                        $= \frac{1}{2}*AB*CX\\\\ =\frac{1}{2}*25cm*8cm\\\\ =25cm*4cm\\\\=100cm^{2}$

Second , In ΔBCD

Base = BC = 16cm , Height = DO = 5cm

Area of ΔBCD  $= \frac{1}{2}*b*h$

                        $= \frac{1}{2}*BC*DO\\\\ =\frac{1}{2}*16cm*5cm\\\\ =8cm*5cm\\\\=40cm^{2}$

From ΔABC & ΔBCD, we get

Area of Quadrilateral = Area of ΔABC + Area of ΔBCD

                                   =  100$cm^{2}$ + 40$cm^{2}$

                                   =  140 $cm^{2}$    Ans.