Question

2. Construct a quadrilateral ABCD with the following measurements.
AB = 6 cm, BC = 6.5 cm, CD = 4.5 cm, DA = 4.5 cm, BD = 6.8 cm​

Answer 1

Answer:

Given:

• AB = 6 cm
• BC = 4 cm
• CD = 5 cm
• DA = 4.5 cm
• ∠ ABC = 100°

Steps for construction

• Step 1 : Draw a rough diagram and mark the given measurments.
• Step 2 : Draw a line segment BC = 4 cm.
• Step 3 : At B on $\overline{BC}$ make ∠ CBX whose measure is 100°
• Step 4 : With B as centre and radius 6 cm draw an arc. This cuts $\overline{BX}$ at A. Join $\overline{CA}$
• Step 5 : With C and A as centres, draw arcs of radii 5 cm and 4.5 cm respectively and let them cut at D.
• Step 6 : Join $\overline{CD}$and $\overline{AD}$. ABCD is the required quadrilateral.
• Step 7 : From B draw $\overline{BF}$⊥ $\overline{AC}$and from D draw $\overline{DE}$⊥ $\overline{AC}$. Measure the lengths of BF and DE. BF = h

1

= 3 cm, DE = h

2

= 2.7 cm and AC = d = 7.8 cm.

Calculation of area:

In the quadrilateral ABCD, d = 7.8 cm, h

1

= 3 cm and h

2

= 2.7 cm.

Area of the quadrilateral ABCD =

2

1

d(h

1

+h

2

)

=

2

1

(7.8)(3+2.7)

=

2

1

×7.8×5.7

=22.23 cm

2

Answer 2

Answer:

Here is your Answer with Correct Measurements !