Mensuration Exercises 16.4

Mensuration Exercises 16.4

Today our topic of discussion is Mensuration Exercises 16.4.

Mensuration Exercises 16.4

 

Mensuration Exercises 16.4

 

Exercises 16.4

  1. The length and witdth of two adjacent sides of a parallelogram are 7 cm, and 5 c.m. respectively. What is the half of its perimeter in cm ?

1) 12

2) 20

3) 24

4) 28

  1. The length of the side of an equilateral triangle is 6 cm. What is its area. (c, m²)

1) 3√3

2) 4√3

3) 6√3

4) 9√3

  1. In plane geometry:

(i) Each angle of equilateral triangle is less than one right angle.

(ii) Sum of acute angles of a right-angled triangle is one right angle.

(ii) An exterior angle of a triangle formed by extending one side of triangle is greater than each of the opposite interior angle.

Which of the following is true?

1) i and ii

2) i and iii

3) ii and iii

4) i ii and iii

  1. If the length of each side of a square is a and diagonal is d, then:

(i) Its area is a² square units

(ii) Perimeter is 2ad units

(iii) d = √2 * a

Which of the following is true?

1) i and ii

2) i and iii

3) ii and iii

4) i, ii and iii

Answer the following questions (5-7) as per information from the picture below:

 

Mensuration Exercises 16.4

 

  1. What is the length of the diagonal of the rectangle ABCD in cm?

1) 13

2) 14

3) 14.4

4) 15

  1. What is the area of the triangle ADF in square em?

1) 16

2) 32

3) 64

4) 128

  1. What is the circumference of the half circle AGB in cm?

1) 18

2) 18.85 (approx.)

3) 37.7 (approx.)

4) 96

  1. The length, width and height of a rectangular solid are 16 metre, 12 metre and 4.5 metre respectively. Determine the area of its whole surface, length of the diagonal and the volume.
  2. The ratios of the length, width and height of a rectangular solid are 21: 16: 12 and the length of diagonal is 87 cm. Determine the area of the whole surface of the solid.
  3. A rectangular solid is standing on a base of area 48 square metre. Its height is 3 metre and diagonal is 13 metre. Determine the length and width of the rectangular solid.
  4. The outer measurements of a rectangular wooden box are 8 cm., 6 cm. and 4 cm., respectively and the area of the whole inner surface is 88cm². Find the thickness of the wood of the box.
  5. The length of a wall is 25 metre, height is 6 metre. and breadth is 30 cm. The length, breadth and height of a brick is 10 cm 5 cm and 3 cm. respectively. Determine the number of bricks required to build the wall with the bricks.
  6. The area of the surface of a cube is 2400 square cm. Determine the diagonal of the cube.
  7. The radius of the base of a cylinder with height 12 cm, is 5 cm. Find the area of the whole surface and the volume of the cylinder.
  8. The area of a curved surface of a right circular cylinder is 100 square cm. and its volume is 150 cubic cm. Find the height and the radius of the cylinder.
  9. The area of the curved surface of a right circular cylinder is 4400 square cm. If its height is 30 cm., find the area of its whole surface.
  1. The inner and outer diameter of a iron pipe is 12 cm and 14 cm respectively and the height of the pipe is 5 metre Find the weight of the iron pipe where weight of 1 cm³ iron is 7.2 gm.
  2. The length and the breadth of a rectangular region are 12 metre and 5 metre respectively. There is a circular region just around the rectangle. The places which are not occupied by the rectangle, are planted with grass.

1) Describe the information above with a figure.

2) Find the diameter of the circular region.

3) If the cost of planting grass per sq. metre is Tk. 50, find the total cost. 19.

   19. The figure is composed of a square and a circular segment.

 

Mensuration Exercises 16.4

 

1) Determine the length of the diagonal and perimeter of the square.

2) Find the total area of the whole region,

3) If a regular hexagon having sides equal to the length of the square is inscribed in a circle, then determine the area of the unoccupied region of the circle. B

  1. ABCD is a parallelogram and BCEF is a rectangle and BC is the base of both of them.

1) Draw a figure of the rectangle and the parallelogram assuming the same height.

2) Show that the perimeter of ABCD is greater than the perimeter of BCEF.

3) Ratio of length and width of the rectangle is 5:3 and its perimeter is 48 metre. Determine the area of the parallelogram

  1. The perimeters of a square region and a rectangular region are same. The length of the rectangle is 3 times of its width and its area is 1200 square metre.

1) Determine the perimeter of the rectangle using the variable r.

2) Determine the area of the square region.

3) Consider a 1.5 metre wide path just around the rectangular region. How many 25 x 12.5 square cm bricks will be required to make the path metalled?

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