Question

Draw a quadrilateral of the measurements AB=8cm, BC=6.5 , <A=50° ,B=65°,AD=5cm. Draw a triangle of the same area ?​

Answer 1

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=6.5 cm.

Step 3 : At A on

AB

make ∠BAXwhose measure is 40

∘

and at B on

AB

make ∠ABYwhose measure is 50

∘

. They meet at C.

Step 4 : With A and C as centres draw two arcs of radius 5 cm 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

=21.25cm

2