Areas & Volumes

1. Pythagorean Theorem (Pythagoras' Theorem)

In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. c2 = a2 + b2 where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Length of the longest rod that can be placed in a box of length l, breadth b and height h = ?l2 + b2 + h2.
Pi is a mathematical constant which is the ratio of a circle's circumference to its diameter. It is denoted by ? (? ? 3.14 ? 22/7)
Sum of Interior Angles of a polygon = 1800 (n ? 2); where n = number of sides

Example: Number of sides of a triangle = 3.

Hence, sum of the interior angles of a triangle = 180(3 ? 2) = 180 × 1 = 180°

Example: Number of sides of a quadrilateral = 4

Hence, sum of the interior angles of any quadrilateral = 180(4 ? 2) = 180 × 2 = 360°

If each of side of a rectangle or any two dimensional shape is increased by x%, its area is increased by (x2/100 + 2x)%
If radius of a circle is increased by x%, its area is increased by (x2/100 + 2x)%

Example: If each side of a triangle is doubled, what is the percentage increase in its area?

Here, each side is increased by 100% (because each side is doubled) percentage increase in its area = (1002/100 + 2 × 100)% = 300%
Example: If circumference of a circle is increased by 50%, what is the percentage increase in its area?

Circumference of the circle is increased by 50%. Since circumference of the circle is 2?r, radius, r is increased by 50%
Percentage increase in its area = (502/100 + 2 × 50)% = 125%

RECTANGLE

SQUARE

PARALLELOGRAM

RHOMBUS

⚡ Recently practiced quizzes in this class

Quantitative Aptitude Practice Test: Time and Distance Quantitative Aptitude Practice Test: Power Cycle Quantitative Aptitude Test 2 Quantitative Aptitude Practice Test: Alligation or Mixture Quantitative Aptitude Practice Test: HCF & LCM Ratio and Proportion Quantitative Aptitude Practice Test: Simplification And Simplification Word Problems Time - Speed and Distance Quantitative Aptitude Practice Test: Average Quantitative Aptitude Practice Test: Ratio and Proportion