Math, asked by Sanjanajadhav17, 5 months ago

construct a quadrilateral ABCD in which AB=5cm,BC=6.5cm,angle A=angle C=100° and ane D=75°​

Answers

Answered by rathoreyashasvi430
1

Step-by-step explanation:

Given:

AB = 6.5 cm, AD = 5 cm, CD = 5 cm, ∠ BAC = 40

o

and ∠ ABC = 50

o

.

Steps for construction

Step 1 : Draw a rough diagram and mark the given measurements.

Step 2 : Draw a line segment AB = 6.5cm.

Step 3 : At A on

AB

make ∠BAX whose measure is 40

0

and at B on

AB

make ∠ABY whose measure is 50

0

. They meet at C.

Step 4 : With A and C as centres draw two arcs of radius 5cm and let them cut at D.

Step 5 : Join

AD

and

CD

. ABCD is the required quadrilateral.

Step 6 : From D draw

DE

AC

and from B draw

BC

AC

. Then measure the lengths of BC and DE. BC = h

1

= 4.2 cm, DE = h

2

= 4.3 cm and AC = d = 5 cm.

Calculation of area:

In the quadrilateral ABCD, d = 5 cm, h

1

= 4.2 cm and h

2

= 4.3 cm.

Area of the quadrilateral ABCD =

2

1

d(h

1

+h

2

)

=

2

1

(57.8)(4.2+4.3)

=

2

1

×5×8.5

=21.25 cm

2

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