Question

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

CUTE with `bar("CU") || bar("ET")`, CU = 7 cm, ∠UCE = 80° CE = 6 cm and TE = 5 cm

Answer 1

Given: In the trapezium CUTE,

CU = 7 cm, ∠UCE = 80°,

CE = 6 cm,TE = 5 cm and `bar("CD") || bar("ET")`

Rough Diagram


Construction:

Steps:

1. Draw a line segment CU = 7 cm

2. Construct an angle ∠UCE = 80° at C

3. With C as centre, draw an arc of radius 6 cm cutting CY at E

4. Draw EX parallel to CU

5. With E as centre, draw an arc 7 cm of radius 5 cm cutting EX at T

6. Join UT.

7. CUTE is the required trapezium.

Calculation of area:

Area of the trapezium CUTE = `1/2 xx "h" xx ("a" + "b")  "sq.units"`

= `1/2 xx 5.9 xx (7 + 5)  "sq.units"`

= 35.4 sq.cm