# 10 Basic Points to Remember for a Good Performance in Mensuration

A comprehensive idea of mensuration including various shortcut tips and tricks can be pretty beneficial for students in the long run especially when they are ready to involve themselves in competitive exams where time is of the essence. Individual shortcut techniques can give the candidate an edge over others because s/he would be able to perform quicker and sharper than others. The same candidate should also be more accurate in his/her answers, thanks to the shortcut techniques and tricks.

In this article, we will discuss a few mensuration points as well as shortcut tips and techniques that should benefit a student for their school exams and also in the long run. Let’s begin.

1. Square

A square that has all equal sides must have four equal angles, each of which should be equal to 90°.

2. Rectangle

A rectangle is having equal opposite sides also have 4 equal angles equal to 90°.

3. Arc of a circle

A curved portion of a circle is called an arc.

4. Equilateral triangle

Equilateral triangle’s a triangle having three equal sides with each of its angle equal to 60°.

5. Isosceles Triangle

It’s a triangle having two equal sides.

In an isosceles right angled triangle, the two equal sides always make an angle of 90° with one another.

If perimeter of any isosceles triangle is considered to be “P” and the base of the triangle is taken to be “b”, the length of its equal sides should be:

(P - b)/2.

If perimeter of an isosceles triangle is considered to be P and the length of the equal sides is considered to be “a,” the base is considered to be:

(P - 2a)

If perimeter (p) and area (A) of a rectangle are provided then,

Length of a rectangle=

A cyclic quadrilateral is a quadrilateral having all its vertices lying on a single circle.

s= (a + b + c + d)/2.

∠A + ∠B +∠C +∠D = 2π

∠A+∠C = ∠B + ∠D = π

7. Increase in length and breadth of a rectangle

If length and breadth are increased by x% and y% respectively, there will be an increase in the area of the triangle by:

8. Increase in length of the rectangle

If the length of a rectangle is increased by x%, the breadth will decrease by:

This formula applies to those cases where the area of the rectangle has to be same on one hand, and the length has to be increased on the other.

9. Rectangular Park

A rectangular park is l m long & b m broad. 2 paths having w m each are perpendicular to one another inside the park. Area of the paths:

w(l+b+2)m2

Also, the area of the park minus the paths:

= (l-w)(b-2)m2

10. Square inscribed within a circle

The area of a square that’s inscribed within a circle having a radius “r” is 2r2.

The side of the same square should be (2r)^1/2.

There are several other tips and tricks available on the internet that is related to the topic of mensuration. You can check them out as per your convenience. Online professional math tutors can also help you out in this matter.