Construct a quadrilateral PQRS,where PL = 5 cm, LA= 7 cm, angle P=100°, angle L= 75° and angle A= 70°
Answers
Answer:
cm
2. With L as centre and radius 2.5 cm, draw an arc.
3. With I as centre and radius 4 cm draw another arc to cut the previous arc at T.
4. Join TL and TL
5. With L as centre and radius 4.5 cm, draw an arc.
6. With I as centre and radius 3 cm, draw another arc to cut the previously drawn arc at F.
7. Join FI, FL and TF.
Then, LIFT is the required quadrilateral.
(ii) Steps of construction:
1. Draw OL = 7.5 cm.
2. With L as centre and radius equal to 5 cm cut an arc.
3. With O as centre and radius equal to 10 cm, cut another arc on the arc drawn in step-2 at point D.
4. With L as centre and radius equal to 6 cm, cut another arc.
5. With D as centre and radius equal to 6 cm cut on arc drawn in step-4 at point G.
6. Join LD, LG, OG, OD and DG.
Hencem GOLD is the required quadrilateral.
Steps of construction:
1. Draw BN = 5.6 cm
2. Draw the right bisector XY of BN, meeting BN at O.
3. From O set off along OY and OD = 3.25 cm along OX.
4. Join BN, EN, ND and DB.
Then, BEND is the required rhombus.
EXERCISE : 4.3
1. Construct the following quadrilateral:
(i) Quadrilateral MORE
(ii) Quadrilateral PLAN
MO = 6 cm
PL = 4 cm
OR = 4.5 cm
LA = 6.5 cm
∠M = 60°
∠P = 90°
∠O = 105°
∠A = 110°
∠R = 105°
∠N = 85°
(iii) Parallelogram HEAR
(iv) Rectangle OKAY
HE = 5 cm
OK = 7 cm
EA = 6 cm
KA = 5 cm
∠R = 85°
Sol. (i) Draw a rough sketch of the required quadrilateral and write down its dimensions
Steps of construction:
1. Draw MO = 6 cm
2. Make ∠MOX = 105°
3. With O as centre and radius 4.5 cm, cut off OR = 4.5 cm long OX.
4. Make ∠ORY = 105°
5. Make ∠ZMO = 60° such that arms RY and MZ intersect at E.
Then, MORE is the required quadrilateral
Steps of construction:
1. Draw PL = 4 cm
2. Make ∠XPL = 90°
3. Make ∠YLP = 75°
4. With L as centre and radius 6.5 cm, cut off LA = 6.5 cm along LY.
5. Make ∠ZAL = 110° and let its arm AZ intersect PX at N.
Then, PLAN is the required quadrilateral.
(iii) Steps of construction:
1. Draw HE = 5 cm
2. Make ∠HEX = 85°
3. With A as centre and radius 5 cm draw an arc.
4. Join HR and AR.
Then HEAR is the required parallelgram.
(iv) Make a rough sketch of the required rectangle and write down its