Construct a quadrilateral abcd with AB = 5.5 cm, AD = 6 cm, angle A = 120°, angle D = 90° and angle B = 40°
Answers
Answer:
Given:
AB = 6.5 cm, AD = 5 cm, CD = 5 cm, ∠ BAC = 40oand ∠ ABC = 50o
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
ABmake ∠BAX whose measure is 400
and at B on AB
make ∠ABY whose measure is 500. 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 ADand CD. ABCD is the required quadrilateral.
Step 6 : From D draw
DE⊥ ACand from B draw BC⊥ AC Then measure the lengths of BC and DE. BC = h1= 4.2 cm, DE = h
2= 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 ABCD = 21d(h1+h2 )= 21
(57.8)(4.2+4.3)= 21×5×8.5
=21.25 cm2
Given :a quadrilateral ABCD with AB=5.5 cm , AD=6 CM, angle A =120° , angle D=90° and angle B =40°
To Find : Construct quadrilateral ABCD
Solution:
Step 1 : Draw a line segment AB = 5.5 cm
Step 2 : Draw an angle of 120° using protector at point A on AB
Step 3 : Take a length of 6 cm from A at angle drawn in step 2 and label the other point as D
Step 4 : Draw an angle of 40° at B on AB using protector
Step 5 : Draw an angle of 90° at D on AD using protector such that it intersect angle drawn in step 4 at C
quadrilateral ABCD is constructed
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