Construct a quadrilateral ABCD, when AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.

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Solution

If we consider a triangle ABD from the given data, then
AB = 3 cm
BD = 4 cm
AD = 7.5 cm
AB + BD = 3 + 4 = 7 cm
However, we know that the sum of the lengths of two sides of a triangle is always greater than the third side.
Therefore, construction is not possible from the given data.

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Similar questions

Try to draw quadrilateral ABCD of these specifications:

(i) AB = 7 cm, BC =5 cm, CD = 4 cm, ∠B = 60°, ∠C = 140°.

(ii) AB = 8 cm, BC = 6 cm, CD = 5.5 cm, DA = 3 cm, ∠B = 50°.

(iii) AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm.

Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why?

A B C D

A B = 4 cm, B C = 3.1 cm, C D = 3 cm, A D = 4.2 cm

A C = 5 cm

B D

A B C D

A B = 3 c m

B C = 4 c m

C D = 4 c m

D A = 5 c m

A C = 5 c m

Question 2
Find the area of a quadrilateral ABCD in which AB=3cm,BC=4cm,CD=4cm, DA = 5cm and AC= 5cm.

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