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Question
Construct the following trapeziums with the given measures and also find their area.
AIMS with `bar("AI") || bar("SM")`, = 6 cm, IM = 5 cm, AM = 9 cm and MS = 6.5 cm
Diagram
Solution
Given AI = 6 cm, IM = 5 cm
AM = 9 cm, and `bar("AI") || bar("SM")`
MS = 6.5 cm
Rough Diagram
Construction:
Steps:
1. Draw a line segment AI = 6 cm.
2. With A and I as centres, draw arcs of radii 9 cm and 5 cm respectively and let them cut at M
3. Join AM and IM.
4. Draw MX parallel to AI
5. With M as centre, draw an arc of radius 6.5 cm cutting MX at S.
6. Join AS AIMS is the required trapezium.
Calculation of Area:
Area of the trapezium AIMS = `1/2 xx "h" xx ("a" + "b") "sq.units"`
= `1/2 xx 4.6 xx (6 + 6.5)`
= `1/2 xx 4.6 xx 12.5`
= 28.75 sq.cm
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Constructing a trapezium when its three sides and one diagonal are given
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