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Question

# Construct a trapezium ABCD in which ¯¯¯¯¯¯¯¯AB is parallel to ¯¯¯¯¯¯¯¯¯DC , AB = 10 cm,BC = 5 cm, AC = 8 cm and CD = 6 cm. Find its area.

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Solution

## Given:¯¯¯¯¯¯¯¯AB is parallel to ¯¯¯¯¯¯¯¯¯DC, AB = 10 cm, BC = 5 cm, AC = 8 cm and CD = 6 cm.Steps for construction:Step 1 : Draw a rough diagram and mark the given measurements.Step 2 : Draw a line segment AB = 10 cm.Step 3 : With A and B as centres draw arcs of radii 8 cm and 5 cm respectively and let them cut at C.Step 4 : Join ¯¯¯¯¯¯¯¯AC and ¯¯¯¯¯¯¯¯BC .Step 5 : Draw ¯¯¯¯¯¯¯¯¯CX parallel to ¯¯¯¯¯¯¯¯BA .Step 6 : With C as centre and radius 6 cm draw an arc cutting ¯¯¯¯¯¯¯¯¯CX at D.Step 7 : Join ¯¯¯¯¯¯¯¯¯AD . ABCD is the required trapezium.Step 8 : From C draw ¯¯¯¯¯¯¯¯CE⊥¯¯¯¯¯¯¯¯AB and measure the length of CE. CE = h = 4 cm. AB = a = 10 cm, DC = b = 6 cm.Calculation of area:In the trapezium ABCD, a = 10 cm, b = 6 cm and h = 4 cm.Area of the trapezium ABCD = 12 h(a+b)=12 (4)(10+6)=12× 4 × 16=32cm2

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