Question

Construct a quadrilateral ABCD, when AB = 5.2 cm, BC = 4.5, CD = 4 cm, AD = 5 cm and ∠A = 75°

Answer 1

Given:

• AB = 5.2 cm
• BC = 4.5 cm
• CD = 4 cm
• AD = 5 cm
• ∠A = 75°

Steps of construction:

1. Draw a line segment AB = 5.2 cm.
2. At point A, construct an angle of 75°.
3. From point A along the ray forming the 75° angle, cut off a length AD = 5 cm and mark point D.
4. Join B and C such that BC = 4.5 cm.
5. With center B and radius = 4.5 cm, draw an arc to mark the possible location of C.
6. With center D and radius = 4 cm, draw an arc to intersect the previous arc and mark that point as C.
7. Join BC and CD to complete the quadrilateral ABCD.

The quadrilateral ABCD, with sides AB = 5.2 cm, BC = 4.5 cm, CD = 4 cm, AD = 5 cm and angle ∠A = 75° is constructed by drawing AB first, then constructing angle 75° at A, marking D and locating C as intersection of arcs from B and D with radius BC and CD respectively, then joining all vertices.