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ML Aggarwal Class 7 Solutions Chapter 16 Perimeter and Area Ex 16.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Ex 16.2

Question 1.
Find the area of each of the following parallelogram:

Solution:

Question 2.
Find the area of each of the following triangles:

Solution:

Question 3.
Find the missing values:

Solution:

Question 4.
Find the missing values:

Solution:

Question 5.
In the given figure, ABCD is a parallelogram whose two adjacent sides are 6 cm and 4 cm. If the height corresponding to the base AB is 3 cm, find:
(i) the area of parallelogram ABCD
(ii) the height corresponding to the base AD.

Solution:

Question 6.
In the given figure, ABC is an isosceles triangle with AB = AC = 7.5 cm and BC = 9 cm. If the height AD from A to BC is 6 cm, find:
(i) the area of ∆ABC
(ii) the height CE from C to AB.

Solution:

Question 7.
If the base of a right-angled triangle is 8 cm and the hypotenuse is 17 cm, find its area.
Solution:

Question 8.
In the given figure, ∆ABC is right-angled at B. Its legs are 8 cm and 6 cm. Find the length of perpendicular BN on the side AC.

Solution:

Question 9.
In the given figure, the area of ∆ABE is equal to the area of parallelogram ABCD. If altitude EF is 16 cm long, find the length of the altitude of the parallelogram to the base AB of length 10 cm. What is the area of ∆AMD, where M is mid-point of side DC?

Solution:

Question 10.
In the given figure, ABCD is a rectangle of size 18 cm by 10 cm. In ABEC, ∠E = 90° and EC = 8 cm. Find the area of the shaded region.

Solution:

Question 11.
In the following figures, find the area of the shaded regions:

Solution:

ML Aggarwal Class 7 Solutions Chapter 16 Perimeter and Area Ex 16.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Ex 16.1

Question 1.
ABCD is a square of side 24 cm. EF is parallel to BC and AE = 15 cm. By how much does
(i) the perimeter of AEFD exceed the perimeter of EBCF?
(ii) the area of AEFD exceed the area of EBCF?

Solution:

Question 2.
Nagma runs around a rectangular park 180 m long and 120 m wide at the rate of 7.5 km/ hour. In how much time will she complete five rounds?
Solution:

Question 3.
The area of a rectangular plot is 540 m². if its length is 27 m, find its breadth and perimeter.
Solution:

Question 4.
The perimeter of a rectangular field is 151 m. If its breadth is 32 m, find its length and area.
Solution:

Question 5.
The area of a rectangular plot is 340 m² and its breadth is 17 m. Find the cost of surrounding the plot with a fence at ₹ 5.70 per meter.
Solution:

Question 6.
The area of a square park is the same as that of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.
Solution:

Question 7.
A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also, find which shape encloses more area and by how much?
Solution:

Question 8.
A door of breadth 1 m and height 2 m is fitted in a wall. The length of the wall is 4.5 m and the height is 3.6 m. Find the cost of whitewashing the wall, if the rate of whitewashing the wall is ₹ 20 per m².
Solution:

Question 9.
A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.
Solution:

Question 10.
A carpet of size 5 m × 2 m has 25 cm wide red border. The inner part of the carpet is blue in colour. Find the area of the blue portion. What is the ratio of the areas of red portion to blue portion?
Solution:

Question 11.
A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find:
(i) the area of the verandah.
(ii) the cost of cementing the floor of the verandah at the rate of ₹ 200 per m2.
Solution:

Question 12.
Two crossroads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m and parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of ₹ 105 per m2.
Solution:

Question 13.
A rectangular room is 10 m long and 7.5 m wide. Find the cost of covering the floor with carpet 1.25 m wide at ₹ 250 per metre.
Solution:

Question 14.
Find the cost of flooring a room 6.5 m by 5 m with square tiles of side 25 cm at the rate of ₹ 9.40 per tile.
Solution:

Question 15.
The floor of a room is in the shape of a square of side 4.8 m. The floor is to be covered with square tiles of perimeter 1.2 m. Find the cost of covering the floor if each tile costs ₹ 27.
Solution:

Question 16.
A rectangular plot of land is 50 m wide. The cost of fencing the plot at the rate of ₹ 18 per metre is ₹ 4680. Find:
(i) the length of the plot.
(ii) the cost of leveling the plot at the rate of ₹ 7.6 per m².
Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Check Your Progress

Question 1.
Identify the nets which can be used to make a tetrahedron (cut out copies of the nets and try it):

Solution:

Question 2.
If four cubes each with 2 cm edge are placed side by side, what would the dimensions of the resultant cuboid be?
Solution:

Question 3.
Two dice are placed side by side as shown in the given figure. What would be the total on the face opposite to
(i) 5 + 6
(b) 4 + 3?

Solution:

Question 4.
For the structures given below sketch the front, side, and top view:

Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) A solid having no vertex and no edge is a ………..
(ii) A solid that has congruent and parallel polygons as top and bottom faces and all other faces rectangular is known as ………
(iii) A pyramid having 4 equilateral triangles as its faces is known as ………
(iv) A solid having 3 faces (one curved and two circulars), no vertex and two curved edges are known as ……..
(v) A solid having a circular base and one vertex is called a ………
(vi) A triangular prism has ……… faces, ………… edges and ………. vertices.
(vii) A triangular pyramid has ……… faces, ………. edges and ……… vertices.
(viii) A square pyramid has ……… faces, ……….. edges and ……… vertices.
(ix) The base of a triangular pyramid is a ………
(x) Out of ……….. faces of a triangular prism, ……… are rectangle and ……….. are triangles.
(xi) Out of ……….. faces of a square pyramid, ………. are a triangle and ………. is/are squares.
(xii) Out of ………. faces of a rectangular pyramid, ………. are triangles and the base is a ……….
(xiii) A ……….. is a sort of skeleton – outline in 2-D, which on folding results in a 3-D shape.
(xiv) If the sum of numbers on the two dice thrown together is 9, then the sum of the numbers opposite to these faces is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The faces of a prism are triangular.
(ii) A cube can be treated as a prism.
(iii) A pyramid has only one vertex.
(iv) All the faces, except the base, of a square pyramid are triangular.
(v) A tetrahedron has 3 rectangular faces and 1 rectangle face.
(vi) A square pyramid has 5 faces and one vertex.
(vii) A cone has one vertex, two faces, and one curved edge.
(viii)The shadow of a 3-D object is a 2-D figure.
(ix) A cube can cast a shadow in the shape of a rectangle.
(x) A cube can cast a shadow in the shape of a hexagon.
(xi) In an isometric sketch, the line segments of different lengths can represent the sides of a cube.
(xii) In an oblique sketch of a cuboid, the size of the opposite faces must be different.
(xiii) The top, front and side views of a sphere are different.
(xiv) The adjoining net is of a hexagonal pyramid.

Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 11):
Question 3.
A triangular prism has
(a) 4 vertices and 6 edges
(b) 6 vertices and 9 edges
(c) 6 vertices and 6 edges
(d) 9 vertices and 6 edges
Solution:

Question 4.
A square pyramid has
(a) 4 vertices and 4 faces
(b) 4 vertices and 5 faces
(c) 5 vertices and 4 faces
(d) 5 vertices and 5 faces
Solution:

Question 5.
A solid having 4 (plane) faces, 4 vertices and 6 edges is called a
(a) triangular prims
(b) rectangular prism
(c) triangular pyramid
(d) rectangular pyramid
Solution:

Question 6.
The number of cubes in the given structure is
(a) 12
(b) 10
(c) 9
(d) 8

Solution:

Question 7.
An isometric sheet is made up of dots forming
(a) squares
(b) rectangles
(c) right-angled triangles
(d) equilateral triangles
Solution:

Question numbers 8 to 11 are based on the given figure in which unit cubes are put together to form a structure as shown:

Question 8.
The number of unit cubes in the given structure is
(a) 13
(b) 20
(c) 21
(d) 22
Solution:

Question 9.
The number of unit cubes to be added to make a cuboid of dimensions 4 unit × 4 unit × 2 unit is
(a) 11
(b) 12
(c) 13
(d) 14
Solution:

Question 10.
If the structure is painted on the surface everywhere, then the number of unit cubes having no face painted is
(a) 0
(b) 1
(c) 2
(d) 11
Solution:

Question 11.
The side view of the given structure is

Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes Ex 15.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Ex 15.3

Question 1.
Count the number of cubes in the following structures:

Solution:

Question 2.
What cross-section is made in the following
(i) vertical cut (ii) horizontal cut?
(a) A brick
(b) A round apple
(c) A die
(d) A circular pipe
(e) An ice cream cone
(f) A square pyramid
Solution:

Question 3.
For each solid given below, the three views (1), (2) and (3) are given. Identify for each solid the corresponding top, front and side views:


Solution:

Question 4.
For the solids given below sketch the front, side and top view:

Solution: