Chapter 6 – Measuring Space: Perimeter and Area

66 questions · Class 9 Mathematics

1

Find the area of a quadrant of a circle whose circumference is 66 cm.

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2

Show how we can use two identical copies of a trapezium to make a parallelogram.

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3

Two rectangles have the same area and the same perimeter.

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4

By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied by the height (the same formula as the one given above).

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5

You know that the area of a parallelogram is base × height.

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6

The wheel of a car has an outer radius of 28 cm.

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7

Three problems about fitting congruent shapes together:

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8

Show that the area of a kite is half the product of its diagonals.

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9

(A) What fraction of the rectangle is covered by the circles?

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10

Use the above to make a conjecture about the area occupied by circles fitted into a rectangle in the manner shown.

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11

(A) What fraction of the triangle is shaded?

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12

The figure shows a quarter circle in a square.

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13

In given figure, four semicircles have been drawn within the given square whose side is 2 units.

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14

In given figure we see two concentric circles with a common centre O.

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15

The figure shows nine identical rectangles fitted together to make a large rectangle whose area is 72 cm².Find the perimeter of each small rectangle.

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16

Show that the areas of the shaded blue triangle and the shaded red triangle are equal.

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17

In the figure we see two shaded regions formed by a quarter circle, a semicircle, and a triangle.

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18

In the given figure, we see three triangles within a rectangle.

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19

Given figure shows two circles passing through each other's centres.

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20

In given figure, semicircles have been drawn on all the sides of a right-angled triangle as shown.

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21

An equilateral triangle is inscribed in a circle of radius r.

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22

A square is inscribed in a circle of radius r.

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23

In my school, the playground is too small to have a 400 m track, so the school constructed a 200 m track instead.

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24

What is the difference in radius between the first and second lanes?

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25

A hexagon is inscribed in a circle of radius r.

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26

What is the connection between this question (refer to NCERT page no.

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27

The area of a rectangle can be found when we know the lengths of its sides.

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28

Since ABD and ACD have equal area, you may wonder — Can we divide ABD using straight cuts into two or more pieces that we can then rearrange to exactly cover ACD?

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29

Suppose we are given two polygons P and Q with equal area.

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30

Think of various rectangles with perimeter 40 units (the sides need not be integers).

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