Page 76 - Mathematics Class - X

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7. We know that area of triangle = × (base × height)
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Base of triangle is equal to the circumference of the circle (2pr) and height of triangle is equal to radius of
circle, i.e. r.

OBSERVATIONS
Actual measurements,

1. Base of the triangle = _________ units

2. Height of triangle = _________ units (i.e. radius of the circle)

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3. Area of triangle = × (base × height) sq. units = _________
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4. Area of circle = Area of triangle = _________

INFERENCE

1. Area covered by threads on the circle and the area of triangular shaped figure formed by threads is the same.
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2. Area of the circle = area of triangle ⇒ × 2pr × r = pr 2
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EXTENDED TASK
1. Find the area of a circular table using this activity.
2. Find the areas of flower beds of circular and semi-circular shapes.

APPLICATION
This result can be also used for making circular designs and in estimating the number of circular tiles required to
cover a floor.

Viva-Voce

1. Define a circle.

Ans. A circle is a collection of points which are at a fixed distance from a fixed point.
2. Write the formula for area of a circle.
Ans. Area of a circle = pr .
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3. Name the circles having the same centre and different radii.
Ans. Concentric circles.

4. Find the area of a circle of radius 4 cm.
22 22×16
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Ans. Area of the circle = rπ 2 = × 4× 4 cm = = 50.29 cm 2
7 7
5. If the diameter of a circle is 14 cm, find the area of the circle.
22 14 14 14
Ans. Area of the circle = rπ 2 = × × = 154 cm [Q r = d/2 = ]
2
7 2 2 2

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