Aptitude Shortcut and Formulas of Mensuration (Triangle)

Shortcut and Formulas of Mensuration (Triangle)

Today we are covering Shortcuts and formulas for how to solve Triangle problem in Mensuration. Before moving ahead with formulas of Triangle, let us first understand basics of Mensuration.

MENSURATION-I (Area & Perimeter)

AREA

The area of any figure is the amount of surface enclosed within its bounding lines. Area is always expressed in square units.

UNITS OF MEASURING AREA

• 100 sq Millimeters = 1sq centimeter
• 100 sq centimeter = 1sq decimeter
• 100 sq decimeters = 1sq meter
• 100 sq meters = 1sq decameter or arc
• 10,000 sq meters =1 hectare
• 1,000,000 sq meters = 100 hectares = 1 sq kilometer

Perimeter

The perimeter of a geometrical figure is the total length of the sides enclosing the figure.

Triangles and their formulas

A triangle is a closed figure bounded by three sides. ABC is a triangle.

The sides A         B, BC and AC are respectively denoted by c, a and b.

Area of a triangle (A)

(a) A 1/2 (base x  height)=  (1/2) a x h

(b) 

where formula is known as Hero’s formula. Perimeter (P) = a +b +c =2s.

2. Right Angled Triangle

A triangle having one of its angles equal to 90° is called a right-angled triangle. The side opposite to the right angle is called the hypotenuse.

In a right angled triangle,

(Hypotenuse)² = sum of squares of sides

i.e h^2 = a^2 + b^2

Area (a)= 1/2(product of the sides containing the right angle)

i.e. A = (1/2) ab

3. Equilateral Triangle

A triangle whose all sides are equal is called an equilateral triangle.

Example: Height of an equilateral triangle is 4 3 cm. Find its area.

Sol: Area of equilateral triangle

4. Isosceles Triangle

A triangle whose two sides are equal is an isosceles triangle.

5. Isosceles Right-angled Triangle

An isosceles right-angled triangle has two sides equal with equal sides making 90° to each other.

If the perimeter of an isosceles triangle is P and the base is b, then the length of the equal sides is ( pb/2)

If the perimeter of an isosceles triangle is P and the length of the sides is a, then base is (P−2a).

Example: If the base of an isosceles triangle is 10 cm and the length of equal sides is 13 cm, find its area.

Sol: Area of the isosceles triangle

Here's a short quiz based on the above facts for practicing.