Question

Construct a trapezium ABCD in which AB = 4 cm, BC = 6 cm, CD = 3.5 cm, AD = 4.6 cm and AD || BС.

Answer 1

Given:

Trapezium ABCD with AD || BC.

AB = 4 cm

BC = 6 cm

CD = 3.5 cm

AD = 4.6 cm

Step-wise calculation and construction:

1. Compute PC the remaining part of BC, after marking of AD:

PC = BC – AD

= 6 – 4.6

= 1.4 cm

2. Draw the base BC:

Draw a straight line segment BC = 6 cm.

3. Mark point P on BC so that BP = AD:

From B along BC, measure BP = 4.6 cm and mark P, so PC = 1.4 cm.

4. Locate D intersection of two arcs:

With centre C and radius CD = 3.5 cm, draw an arc.

With centre P and radius = AB = 4.0 cm, draw an arc.

The intersection of these two arcs choose the intersection on the same side of BC where A will lie gives point D.

Justification: After translating AD to start at B, the corresponding point P satisfies BP = AD, and DP must equal AB, so D lies on circle centre P, radius AB and on circle centre C, radius CD. This is the standard construction used for trapezia with one pair of parallel sides. 

5. Locate A:

With centre B and radius AB = 4.0 cm, draw an arc.

With centre D and radius AD = 4.6 cm, draw an arc.

Their intersection the one on the same side of BC as D is A.

6. Complete the trapezium:

Join A to B, A to D and D to C. ABCD is the required trapezium.