Question

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

ARMY with `bar("AR") || bar("YM")`, AR = 7 cm, RM = 6.5 cm ∠RAY = 100° and ∠ARM = 60°

Answer 1

Given: In the trapezium ARMY

AR = 7 cm, RM = 6.5 cm,

∠RAY = 100° and ARM 60°, `bar("AR") || bar("YM")`

Rough Diagram


Construction:

Steps:

1. Draw a line segment AR = 7 cm

2. Construct an angle ∠RAX = 100° at A

3. Construct an angle ∠ARN = 60° at R

4. With R as centre, draw an arc of radius 6.5 cm cutting RN at M

5. Draw MY parallel to AR

6. ARMY is the required trapezium.

Calculation of Area:

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

= `1/2 xx 5.6 xx (7 + 4.8)  "sq.units"`

= `1/2 xx 5.6 xx 1.18`

= 33.04 sq.cm