Construct quadrilateral ABCD, where AB = 6 cm, BC= 7 cm, CD= 4.5 cm, DA= 6.5 cm and angle A= 120 degrees. What is the measure of angle B?
Class 8
Answers
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
BC
make ∠ CBX whose measure is 100 °
.
Step 4 : With B as centre and radius 6 cm draw an arc. This cuts
BX
at A. Join
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 CD and AD
. ABCD is the required quadrilateral.
Step 7 : From B draw
BF ⊥ AC and from D draw
DE⊥ 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 =
1
2 d(h^1 +h ^2 )
=
1
2
(7.8)(3+2.7)
= 1
2 ×7.8×5.7
=22.23 cm ^2