DUTY with DU || YT, DU = 8 cm, ∠DUT = 60°, UT = 6 cm and TY = 5 cm.

Question

Construct the trapeziums with the given measures and also find their area.

DUTY with DU || YT, DU = 8 cm, ∠DUT = 60°, UT = 6 cm and TY = 5 cm.

Answer 1

Given:

In the trapezium DUTY

DU = 8 cm, ∠DUT = 60°,

UT = 6 cm, TY = 5 cm

and DU || YT

Construction:

Steps:

1. Draw a line segment DU = 8 cm.
2. Construct an angle ∠DUT = 60° at U
3. With U as centre, draw an arc of radius 6 cm cutting UA at T.
4. Draw TX parallel to DU
5. With T as centre, draw an arc of radius 5 cm cutting TX at Y
6. Join DE. DUTY is the required trapezium.

Calculation of area:

Area of the trapezium DUTY = 12 x h x (a + b) sq. units

= 12 x 5.2 x (8 + 5) sq. units 

= 12 x 5.2 x 13

= 33.8 sq.cm