Ncert exemplar solutions mathematics class 7 Solutions for Chapter 9 perimeter and area

Observe the shapes 1, 2, 3, and 4 in the figures. Which of the following statements is not correct?

(a) Shapes 1, 3, and 4 have different areas and different perimeters.

(b) Shapes 1 and 4 have the same area as well as the same perimeter.

(c) Shapes 1, 2, and 4 have the same area.

(d) Shapes 1, 3, and 4 have the same perimeter.

A rectangular piece of dimensions 3 cm × 2 cm was cut from a rectangular sheet of paper of dimensions 6 cm × 5 cm (Fig. 9.14).

The area of the remaining sheet of paper is

(a) 30 cm2 (b) 36 cm2 (c) 24 cm2 (d) 22 cm2

36 unit squares are joined to form a rectangle with the least perimeter. The perimeter of the rectangle is

(a) 12 units (b) 26 units (c) 24 units (d) 36 units

A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, its radius is

(a) 22 cm (b) 14 cm (c) 11 cm (d) 7 cm

Area of the circle obtained in Question 4 is

(a) 196 cm2 (b) 212 cm2 (c) 616 cm2 (d) 644 cm2

The area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are 14cm × 11 cm, the radius of the circle is

(a) 21 cm (b) 10.5 cm (c) 14 cm (d) 7 cm.

Area of shaded portion in Fig. 9.15 is

(a) 25 cm2 (b) 15 cm2 (c) 14 cm2 (d) 10 cm2

The area of parallelogram ABCD (Fig. 9.16) is not equal to

(a) DE × DC (b) BE × AD (c) BF × DC (d) BE × BC

Area of triangle MNO of Fig. 9.17 is

(a) ½ MN × NO (b) ½ NO × MO

(c) ½ MN × OQ (d) ½ NO × OQ

The ratio of the area of ∆MNO to the area of parallelogram MNOP in the same figure 9.17 is

(a) 2 : 3 (b) 1: 1 (c) 1: 2 (d) 2: 1

Ratio of areas of ∆MNO, ∆MOP and ∆MPQ in Fig. 9.18 is

(a) 2 : 1 : 3 (b) 1 : 3 : 2 (c) 2 : 3 : 1 (d) 1 : 2 : 3

In Fig. 9.19, EFGH is a parallelogram, altitudes FK and FI are 8 cm and 4cm respectively. If EF = 10 cm, then area of EFGH is

(a) 20 cm2 (b) 32 cm2 (c) 40 cm2 (d) 80 cm2

In reference to a circle, the value of π is equal to

(a) area/circumference (b) area/diameter

(c) circumference/diameter (d) circumference/radius

Area of triangle PQR is 100 cm2 (Fig. 9.20). If altitude QT is 10 cm, then its base PR is

(a) 20 cm (b) 15 cm (c) 10 cm (d) 5 cm

In Fig. 9.21, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is

(a) 6 cm (b) 9 cm (c) 4 cm (d) 2 cm

In Fig. 9.22 ∆ MNO is a right-angled triangle. Its legs are 6 cm and 8 cm long. Length of perpendicular NP on the side MO is

(a) 4.8 cm (b) 3.6 cm (c) 2.4 cm (d) 1.2 cm

Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is

(a) 14 cm (b) 13 cm (c) 12 cm (d) 11cm

Circumference of a circle of diameter 5 cm is

(a) 3.14 cm (b) 31.4 cm (c) 15.7 cm (d) 1.57 cm

Circumference of a circle disc is 88 cm. Its radius is

(a) 8 cm (b) 11 cm (c) 14 cm (d) 44 cm

Length of tape required to cover the edges of a semicircular disc of radius 10 cm is

(a) 62.8 cm (b) 51.4 cm (c) 31.4 cm (d) 15.7 cm

Area of circular garden with diameter 8 m is

(a) 12.56 m2 (b) 25.12 m2 (c) 50.24 m2 (d) 200.96 m2

The area of a circle with diameter ‘m’ radius ‘n’ and circumference ‘p’ is

(a) 2πn (b) πm2 (c) πp2 (d) πn2

A tabletop is semicircular in shape with a diameter of 2.8 m. The area of this tabletop is

(a) 3.08 m2 (b) 6.16 m2 (c) 12.32 m2 (d) 24.64 m2

If 1m2 = x mm2, then the value of x is

(a) 1000 (b) 10000 (c) 100000 (d) 1000000

If p squares of each side 1mm make a square of side 1cm, then p is equal to

(a) 10 (b) 100 (c) 1000 (d) 10000

12 m2 is the area of

(a) a square with side 12 m

(b) 12 squares with side 1m each

(c) 3 squares with side 4 m each

(d) 4 squares with side 3 m each

If each side of a rhombus is doubled, how much will its area increase?

(a) 1.5 times (b) 2 times (c) 3 times (d) 4 times

If the sides of a parallelogram are increased to twice its original lengths, how much will the perimeter of the new parallelogram?

(a) 1.5 times (b) 2 times (c) 3 times (d) 4 times

If the radius of a circle is increased to twice its original length, how much will the area of the circle increase?

(a) 1.4 times (b) 2 times (c) 3 times (d) 4 times

What will be the area of the largest square that can be cut out of a circle of radius 10 cm?

(a) 100 cm2 (b) 200 cm2 (c) 300 cm2 (d) 400 cm2

What is the radius of the largest circle that can be cut out of the rectangle measuring 10 cm in length and 8 cm in breadth?

(a) 4 cm (b) 5 cm (c) 8 cm (d) 10 cm

The perimeter of the figure ABCDEFGHIJ is

(a) 60 cm (b) 30 cm (c) 40 cm (d) 50 cm

The circumference of a circle whose area is 81πr2 is

(a) 9πr (b) 18πr (c) 3πr (d) 81πr

The area of a square is 100 cm2. The circumference (in cm) of the largest circle cut of it is

(a) 5 π (b) 10 π (c) 15 π (d) 20 π

If the radius of a circle is tripled, the area becomes

(a) 9 times (b) 3 times (c) 6 times (d) 30 times

The area of a semicircle of radius 4r is

(a) 8πr2 (b) 4πr2 (c) 12πr2 (d) 2πr2

Perimeter of a regular polygon = length of one side × ___________.

If a wire in the shape of a square is rebent into a rectangle, then the _____________ of both shapes remain same, but ___________may vary.

Area of the square MNOP of Fig. 9.24 is 144 cm2. The area of each triangle is _____.

In Fig. 9.25, the area of parallelogram BCEF is ___________ cm2 where ACDF is a rectangle.

To find the area, any side of a parallelogram can be chosen as ___________of the parallelogram.

Perpendicular dropped on the base of a parallelogram from the opposite vertex is known as the corresponding ____________of the base.

The distance around a circle is its ______________.

The ratio of the circumference of a circle to its diameter is denoted by symbol ________.

If the area of a triangular piece of cardboard is 90 cm2, then the length of altitude corresponding to 20 cm long base is _____________cm.

The value of π is _______________approximately.

Circumference ‘C’ of a circle can be found by multiplying diameter ‘d’ with __________.

Circumference ‘C’ of a circle is equal to 2π × ____________.

1 m2 = 10000 cm2.

1 cm2 = _________mm2.

1 km2 = _______________m2.

Area of a triangle = ½ × base × __________.

1 hectare = ____________m2.

The area of a square of side 6 m is equal to the area of ____________squares of each side 1 cm

10 cm2 = _____________m2.

In Fig. 9.26, the perimeter of (ii) is greater than that of (i), but its area is smaller than that of (i).

In Fig. 9.27,

(a) area of (i) is the same as the area of (ii).

(b) The perimeter of (ii) is the same as (i).

(c) If (ii) is divided into squares of unit length, then its area is 13 unit squares.

(d) The perimeter of (ii) is 18 units.

If perimeter of two parallelograms are equal, then their areas are also equal.

All congruent triangles are equal in the area.

All parallelograms having equal areas have the same perimeters. Observe all the four triangles FAB, EAB, DAB, and CAB as shown in Fig. 9.28:

All triangles have the same base and the same altitude.

All triangles are congruent.

All triangles are equal in area.

All triangles may not have the same perimeter.