Question

Construct a quadrilateral ABCD with AB = 6.5cm, AD = 4.5cm , ∠ A = 60, ∠ B =90 and ∠ C = 120. Find the measurement of CD.

Answer 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

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Answer 2

$\huge\red{Question}$

Q.Construct a quadrilateral ABCD with AB = 6.5cm, AD = 4.5cm , ∠ A = 60, ∠ B =90 and ∠ C = 120. Find the measurement of CD.

$\huge\pink{Answer}$]

Given:

AB = 6.5 cm, AD = 5 cm, CD = 5 cm, ∠ BAC = 40° and ∠ABC = 50°

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° and at B on AB make ∠ABY whose measure is 50°. 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. haaABCD 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 = h1 = 4.2 cm,

DE = h2

= 4.3 cm and AC = d = 5 cm.

Calculation of area:

In the quadrilateral ABCD, d = 5 cm, h1

= 4.2 cm and h2

= 4.3 cm.

Area of the quadrilateral

$haABCD = 21d(h1+h2)$

$=21(57.8(4.2+4.3)$

$= 21×5×8.5$

$=21.25 cm$

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