## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) The perimeter of a regular polygon = ……….. × length of a side.

(ii) The unit of measurement of the area is ……….

(iii) The perimeter of a rhombus is = 4 × ………

(iv) An area of 1 km^{2} = ……… hectare

(v) If the perimeter of a parallelogram is 40 cm and the length of one side is 12 cm, then the length of the adjacent side is ……

(vi) To find the cost of polishing a table-top, we need to find the ………. of the table-top.

(vii) The ratio of circumference to the diameter of a circle is ………..

(viii) If the area of a triangular piece of cardboard is 90 cm^{2}, then the length of the altitude corresponding to 20 cm long base is ………. cm.

Solution:

Question 2.

State whether the following statements are true (T) or false (F):

(i) A diagonal of a rectangle divides it into two right-angled triangles of equal areas.

(ii) A diagonal of a parallelogram divides it into two triangles of equal areas.

(iii) If the perimeter of two parallelograms is equal, then their areas are also equal.

(iv) All parallelogram having equal areas have the same perimeters.

(v) The area of a circle of diameter d is πd^{2}.

(vi) Area of a parallelogram = product of lengths of its two adjacent sides.

Solution:

**Multiple Choice Questions**

Choose the correct answer from the given four options (3 to 14):

Question 3.

If the perimeter of a square is 24 cm, then its area is

(a) 16 cm^{2}

(b) 24 cm^{2}

(c) 36 cm^{2}

(d) 36 m^{2}

Solution:

Question 4.

If the area of a parallelogram is 54 cm^{2} and the length of one side is 7.5 cm, then the corresponding height is

(a) 7.2 cm

(b) 14.4 cm

(c) 3.6 cm

(d) 13.5 cm

Solution:

Question 5.

If the base of a triangle is doubled and its height is halved, then the area of the resulting triangle

(a) decreases

(b) increases

(c) doubles

(d) remains the same

Solution:

Question 6.

If the height of a parallelogram is doubled and base tripled, then its area becomes

(a) 2 times

(b) 3 times

(c) 6 times

(d) 12 times

Solution:

Question 7.

The circumference of the circle with diameter 28 cm is

(a) 44 cm

(b) 88 cm

(c) 176 cm

(d) 616 cm

Solution:

Question 8.

The ratio of circumference to the area of a circle of radius r units is

(a) 2 : r

(b) r : 2

(c) 1 : r

(d) π : r

Solution:

Question 9.

If the area of a circle is numerically equal to its circumference, then the radius of the circle is

(a) 1 unit

(b) 2 units

(c) 3 units

(d) 4 units

Solution:

Question 10.

The area of a circle of diameter d is

(a) 2πd^{2}

(b) πd^{2}

(c) \(\frac { \pi { d }^{ 2 } }{ 2 }\)

(d) \(\frac { \pi { d }^{ 2 } }{ 4 }\)

Solution:

Question 11.

If the ratio of the radii of two circles is 2 then the ratio of their circumferences is

(a) 2 : 3

(b) 3 : 2

(c) 4 : 9

(d) 9 : 4

Solution:

Question 12.

If the ratio of the radii of two circles is 3 : 5, then the ratio of their areas is

(a) 3 : 5

(b) 5 : 3

(c) 25 : 9

(d) 9 : 25

Solution:

Question 13.

The perimeter of a semicircle (including its diameter) of radius 7 cm is

(a) 22 cm

(b) 29 cm

(c) 36 cm

(d) 44 cm

Solution:

Question 14.

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

(a) 21 cm

(b) 14 cm

(c) 10.5 cm

(d) 7 cm

Solution:

**Higher Order Thinking Skills (HOTS)**

Question 1.

In the given figure, ABDE is a parallelogram, find the area of the trapezium ACDE.

Solution:

Question 2.

In the given figure, the length of the rectangle is 28 cm. Find the area of the shaded region.

Solution:

Question 3.

In the given figure, ABCD is a square of side 14 cm. A, B, C, and D are centers of circular arcs of equal radius. Find the perimeter and the area of the shaded region.

Solution: