Mathematics
Asifa cut an aeroplane from a coloured chart paper (as shown in the adjoining figure). Find the total area of the chart paper used, correct to 1 decimal place.
Mensuration
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Answer
The points are labelled as shown in the figure below:
In △ABK,
a = BK = 1 cm, b = AK = 5 cm and c = AB = 5 cm.
s = = 5.5 cm.
Area of △ABK =
Substituting values we get,
Area of △KIJ = base × height
= × KI × KJ
= × 1.5 × 6
= 4.5 cm2.
Area of △CBD = base × height
= × BD × CB
= × 1.5 × 6
= 4.5 cm2.
Area of rectangle BKHE = length × breadth
= BE × EH
= 6.5 × 1 = 6.5 cm2.
Let EL and HM be perpendicular to LM.
Since, EFGH is an isosceles trapezium so,
FL = MG = = 0.5 cm.
In right angle △EFL,
⇒ EF2 = EL2 + FL2
⇒ 12 = EL2 + (0.5)2
⇒ EL2 = 12 - (0.5)2
⇒ EL2 = 1 - 0.25
⇒ EL2 = 0.75
⇒ EL = = 0.87 cm.
Area of trapezium EFGH = × (sum of parallel sides) × distance between them
= × (EH + FG) × EL
= × (1 + 2) × 0.87
= 1.3 cm2.
Area of chart paper used = Area of aeroplane = Area of △ABK + Area of △KIJ + Area of △CBD + Area of rectangle BKHE + Area of trapezium EFGH
= 2.5 + 4.5 + 4.5 + 6.5 + 1.3
= 19.3 cm2.
Hence, area of chart paper used = 19.3 cm2.
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