Construct a quadrilateral ABCD of which AB = 4 cm, BC = 8 cm, CD = 6 cm, AD = 4 cm, AC = 9.5 cm. Then construct a triangle of area equal to the area of ABCD. Find the dimensions of the triangle [Use Construction]

(4, 11, 12) cm

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(13, 13, 13) cm

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(15, 6, 9) cm

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(6, 6, 6) cm

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Solution

The correct option is A
(4, 11, 12) cm

Method of Construction:
(1) Construct a quadrilateral ABCD of which AB = 4 cm, BC = 8 cm, CD = 6 cm, AD = 4 cm, AC = 9.5 cm.
(2) Draw DG through D parallel to AC
(3) Produce BC in such a way that it intersects DG at E.
(4) A, E are joined.
$∴ Δ A B E$ is the required triangle, which measures (4, 11, 12) cm. [approx]

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Question 1
Construct the Quadrilateral ABCD where
AB=4.5 cm, BC=5.5 cm, CD=4 cm,AD=6cm, AC=7 cm

Construction of a unique quadrilateral ABCD is possible with AB = 4cm, BC = 6cm, AC = 7cm, CD = 5cm and BD = 8cm.

A B = 8 c m, B C = 5 c m, A C = 6 c m, C D = 4.5 c m

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