Question

in a quadrilateralABCD diagonal AC 44 cm and the length of the perpendicular from a on AC are 20 cm and 15 CM respectively find the area of quadrilateral​

Answer 1

Answer:

Area of the Quadrilateral ABCD = 770 $cm^{2}$

Step-by-step explanation:

 Given:

ABCD is a Quadrilateral.

Length of Diagonal AC is 6cm.

Perpendicular BM from Vertex B is 20cm.

Perpendicular DN from Vertex D is 15cm.

To Find:

Area of Quadrilateral ABCD.

Concept:

Here, we are given a Quadrilateral which has a diagonal and two perpendiculars of different lengths are dropped on the same diagonal. The diagonal cuts the quadrilateral into two different triangles. Finding the area of both triangles and adding them will give us the Area of Quadrilateral needed.

Formula Used:

Area of a Triangle = 1/2 * b * h...….(I)

where b = base of the triangle and h = height of the triangle

Solution:

Let's firstly find out the area of triangle ABC.

» Base of ∆ABC= 44cm.

» Height of ∆ABC= 20cm.

Equating the values in Formula (I) . We get,

Area of the ∆ABC = (1/2 * 44 * 20)

                              = 22 * 20 = 440 $cm^{2}$

Now, Let's find the Area of triangle ADC.

» Base of ∆ADC= 44cm.

» Height of ∆ADC= 15cm.

Equating the values in Formula (I) . We get,

Area of the ∆ADC = (1/2 * 44 * 15)  

                               =  22 * 15 = 330 $cm^{2}$

Now, adding the Areas of ∆ABC and ∆ADC gives Area of Quadrilateral ABCD.

So,  Area of the Quadrilateral ABCD = Area of the ∆ABC + Area of the ∆ADC

                                                            =  440 $cm^{2}$ + 330 $cm^{2}$ = 770 $cm^{2}$