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Question

Construct a quadrilateral ABCD with AB = 6 cm, BC = 4 cm, CD = 5 cm, DA = 4.5 cm, EABC = 100 and find its area.

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Solution

Given:
AB = 6 cm, BC = 4 cm, CD = 5 cm, DA = 4.5 cm ABC = 100o .
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 100o .
Step 4 : With B as centre and radius 6 cm draw an arc. This cuts
¯¯¯¯¯¯¯¯¯BXat 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
¯¯¯¯¯¯¯¯¯CDand ¯¯¯¯¯¯¯¯¯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 = h1 = 3 cm, DE = h2 = 2.7 cm and AC = d = 7.8 cm.
Calculation of area:
In the quadrilateral ABCD, d = 7.8 cm, h1 = 3 cm and h2 = 2.7 cm.
Area of the quadrilateral ABCD = 12d(h1+h2)
=12(7.8)(3+2.7)
=12×7.8×5.7
=22.23 cm2
754760_616513_ans_ea44d286e78c473ebca167ebdca63ada.png

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