EXERCISE 18 B 1. Construct a quadrilateral ABCD, given that AB = 6.5 cm, AD = 4.5 cm, ZA = 60°, ZB = 90° ZC = 120°. A = 75° C = 105° an חם - 65 cm
Answers
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 = 6.5cm.
Step 3 : At A on AB make ∠BAX whose measure is 40° and at B on AB make ∠ABY whose measure is 50°. 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 AD and CD. haaABCD 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 = h1 = 4.2 cm,
DE = h2
= 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
haABCD = 21d(h1+h2)haABCD=21d(h1+h2)
=21(57.8(4.2+4.3)=21(57.8(4.2+4.3)
= 21×5×8.5=21×5×8.5
=21.25 cm=21.25cm
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