Question

5. Aman's field is as shown below. He wants to grow pulses in his field. Find the total area where he can grow the pulses?

Answer 1

Answer:

1098 area

I think .

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Answer 2

The total area in which Aman can grow the pulses is 203.7$cm^{2}$

Given:

Given that AF = 9cm, AG = 13cm, AH = 19cm, AD = 24cm,

BF = 6cm, CH = 8cm , EG = 9cm.

To Find:

The total area of Aman's field.

Solution:

In order to find the total area, we will consider Aman's field to be a combination of four triangles, ΔACH, ΔDCH, ΔAEG and ΔDEG.

Each of these triangles are right angled triangles.

Area of a triangle = $\frac{1}{2}$× base× height

So, area of ABCDEA =area(ΔACH) +area(ΔDCH)+ area(ΔAEG)+ area(ΔDEG)

In ΔACH,

Base AH= 19cm

Height CH = 8cm

Hence area(ΔACH)= $\frac{1}{2}$× base× height= $\frac{1}{2}$× 19× 8= 76$cm^{2}$

In ΔDCH,

Base DH= AD-AH= 24-19= 5

Height CH = 8cm

Hence area(ΔDCH) = $\frac{1}{2}$× base× height= $\frac{1}{2}$× 5× 8= 20$cm^{2}$

In ΔAEG,

Base AG= 13cm

Height EG= 9cm

Hence area(ΔAEG) = $\frac{1}{2}$× base× height=  $\frac{1}{2}$×13×9= 58.2$cm^{2}$

In ΔDEG,

Base DG= AD-AG=24-13= 11cm

Height EG= 9cm

Hence area(ΔAEG) = $\frac{1}{2}$× base× height=  $\frac{1}{2}$×11×9= 49.5$cm^{2}$

Hence total area (ABCDEA) =area(ΔACH) +area(ΔDCH)+ area(ΔAEG)+ area(ΔDEG)= 76+20+58.2+49.5= 203.7$cm^{2}$

Therefore the total area in which Aman can grow the pulses is 203.7$cm^{2}$.

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