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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Question

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.

KnowledgeBoat · Accepted 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.

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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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

Related Questions

Find the area of the quadrilateral ABCD shown in figure (ii) given below. All measurements are in centimeters.

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From a square cardboard, a circle of biggest area was cut out. If the area of the circle is 154 cm², calculate the original area of the cardboard.