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Question
Construct the following trapeziums with the given measures and also find their area.
CITY with `bar("CI") || bar("YT")`, CI = 7 cm, IT = 5.5 cm, TY = 4 cm and YC = 6 cm
Solution
Given: In the trapezium CITY,
CI = 7 cm, IT = 5.5 cm, TY = 4 cm
YC = 6 cm, and `bar("CI") || bar("YT")`
Rough Diagram
Construction:
Steps:
1. Draw a line segment CI = 7 cm.
2. Mark a point D on CI such that CD = 4 cm
3. With D and I as centres, draw arcs of radii 6 cm and 5.5 cm respectively.
4. Let them cut at T. Join DT and IT.
5. With C as centre, draw an arc of radius 6 cm.
6. Draw TY parallel to Cl. Let the line cut the previous arc at Y.
7. Join CY. CITY is the required trapezium.
Construction of area:
Area of the trapezium CITY = `1/2 xx "h" xx ("a" + "b") "sq.units"`
= `1/2 xx 5.5 xx (7 + 4) "sq.units"`
= `1/2 xx 5.5 xx 11`
= 30.25 sq.cm
