## Geometry and Mensuration – Aptitude Basics, Formulas, Concepts!!

## Geometry and Mensuration

Mensuration is the mathematics branch that deals with the analysis of geometric shapes, its area, distance, and various geometric object parameters. “Geo” means “Earth,” and “Metry” means “Measure.”Geo – metry, therefore, is simply ‘Measurement of earth ‘ Traditional geometric concepts are called Euclidean geometry (principally in two dimensions).

### Important Formulas

- Area of rectangle (A) = length(l) * Breath(b);
- Perimeter of a rectangle (P) = 2 * (Length(l) + Breath (b))
- Area of a square (A) = Length (l) * Length (l)
- Perimeter of a square (P) = 4 * Length (l)
- Area of a parallelogram(A) = Length(l) * Height(h)
- Perimeter of a parallelogram (P) = 2 * (length(l) + Breadth(b))
- Area of a triangle (A) = (Base(b) * Height(b)) / 2

And for a triangle with sides measuring “a” , “b” and “c” , Perimeter = a+b+c and s = semi perimeter = perimeter / 2 = (a+b+c)/2

This formula is also known as “Hero’s formula.”

Where a = length of two equal sides, b= length of the base of the isosceles triangle.

- Area of trapezium (A) =(a+b)/2

Where “a” and “b” are the length of parallel sides.

- The perimeter of a trapezium (P) = sum of all sides
- Area f rhombus (A) = Product of diagonals / 2
- The perimeter of a rhombus (P) = 4 * l, where l = length of a side
- Area of quadrilateral (A) = 1/2 * Diagonal * (Sum of offsets)

- Area of a Kite (A) = 1/2 * product of its diagonals
- The perimeter of a Kite (A) = 2 * Sum on non-adjacent sides
- Area of a Circle (A) =

where r= radius of the circle

- Circumference of a Circle =

r= radius of the circle

d= diameter of the circle

- Total surface area of cuboid = 2(lb+bh+lh) where , l= length , b=breadth , h=height
- The total surface area of cuboid = 6l
^{2 }where, l= length - length of diagonal of cuboid =

- Length of diagonal of cube =

- Volume of cuboid = l * b * h
- The volume of cube = l * l* l
- Area of base of a cone =
- The curved surface area of a cone =C Where , r = radius of the base , l = slanting height of the cone
- The total surface area of a cone =

- The volume of right circular cone =

Where , r = radius of the base of the cone , h= height of the cone (perpendicular to base)

- The surface area of triangular prism = (P * height) + (2 * area of a triangle) Where, p = perimeter of the base
- The surface area of polygonal prism = (Perimeter of base * height ) + (Area of polygonal

base * 2) - The lateral surface area of prism = Perimeter of base * height
- The volume of Triangular prism = Area of the triangular base * height
- The curved surface area of a cylinder =

Where, r = radius of the base, h = height of the cylinder

- The total surface area of a cylinder =

- The volume of a cylinder =

- The surface area of sphere =

where, r= radius of the sphere, d= diameter of the sphere

- The volume of a sphere =

- The volume of hollow cylinder =

where , R = radius of cylinder , r= radius of hollow , h = height of cylinder

- The surface area of a right square pyramid =

Where a = length of the base, b= length of equal side, of the isosceles triangle forming the slanting face.

- The volume of a right square pyramid =

- Area of a regular hexagon =

- Area of equilateral triangle =

- The curved surface area of a Frustums =

- The total surface area of a Frustums =

- The curved surface area of a Hemisphere =

- The total surface area of a Hemisphere =

- The volume of a Hemisphere =

- Area of a sector of a circle =

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### Aptitude-Geometry and Mensuration Questions & Answers

**1. 5 cm of rainfall, in a shower. The volume of water falling on 1.5 hectares of land is as follows:**

- A. 75 cu. m
- B. 750 cu. m
- C. 7500 cu. m
- D. 75000 cu. m

**Answer:** Option B (750 cu. m)

**2. How many tiles with a length and width of 12 cm and 5 cm respectively are required to fit in a rectangular area with a length and width of 144 cm and 100 cm, respectively:**

- A. 160
- B. 240
- C. 320
- D. 450

**Answer:** Option B (240)

**3. Rectangle sides are in the ratio 4:3, and its area is 972sq.m to find the rectangle perimeter?**

- A. 120m
- B. 122m
- C. 124m
- D. 126m

**Answer:** Option D (126m)

**4. It is necessary to paint the four walls and ceiling of a room-length 25 ft., breadth 12 ft. and height 10 ft. Painter A can paint 200 sqr.ft within five days, and painter B can paint 250 sqr.ft within two days. If A & B work together, how many days will they be completing the job?**

- A. 5 8/13
- B. 5 11/12
- C. 6 10/33
- D. 7 6/11

**Answer:** Option C (6 10/33)

**5. A hall is 15 m long and 12 m tall. If the sum of the floor and ceiling areas is equal to the sum of the four wall surfaces, the hall volume is:**

- A. 720
- B. 900
- C. 1200
- D. 1800

**Answer:** Option C (1200)

**6. Four maximum circular plates of equal size are cut off from a 784 cm2 square paper sheet. Every plate has a circumference of:**

- A. 22 cm
- B. 44 cm
- C. 66 cm
- D. 88 cm

**Answer:** Option B (44 cm)

**7. In a semicircle of a 7 cm radius is inscribed a right-angled isosceles triangle. The area enclosed to the triangle by the semicircle but outside is**

- A. 14 sq cm
- B. 28 sq cm
- C. 44 sq cm
- D. 68 sq cm

**Answer:** Option B (28 sq cm)

**8. A hollow iron pipe is 21 cm wide, with an outer diameter of 8 cm. If the pipe diameter is 1 cm and iron weighs 8 g / cm3, then the pipe weight is:**

- A. 3.6 kg
- B. 3.696 kg
- C. 36 kg
- D. 36.9 kg

**Answer:** Option B (3.696 kg)

**9. A boat measuring 3 m in length and 2 m in breadth floats on a lake. When a man gets on it, the boat sinks by 1 cm. The Mass of the Man is:**

- A. 12 kg
- B. 60 kg
- C. 72 kg
- D. 96 kg

**Answer:** Option B (60 kg)

**10. What is the total surface area of a 14 cm high, right circular cone, and 7 cm base radius?**

- A. 344.35 cm2
- B. 462 cm2
- C. 498.35 cm2
- D. None of these

**Answer:** Option C (498.35 cm2)