# Mensuration Tricks

इस पोस्ट में हम कुछ सबसे महत्वपूर्ण क्षेत्रमिति ट्रिक्स (Mensuration Tricks) साझा करने जा रहे हैं। यह उन छात्रों और शिक्षार्थियों के लिए बहुत उपयोगी Mensuration Short Tricks है जो विभिन्न प्रकार की प्रतियोगी परीक्षा को क्रैक करना चाहते हैं। इन ट्रिक्स को सीखने से पहले आपको क्षेत्रमिति (Mensuration) की परिभाषा और मूल शब्द सीखना होगा।

Mensuration: Mensuration is the science of measurement of the lengths of lines, areas of surfaces and volumes of solids.

Perimeter:  Perimeter is sum of all the sides. It is measured in cm, m, etc.

Area: The area of any figure is the amount of surface enclosed within its boundary lines.

Volume: If an object is solid, then the space occupied by such an object is called its volume.

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## Mensuration Maths Tricks

Mensuration Formulas List

Square:

• Area of square = a x a
• Perimeter of square = 4a

Here, a = side of square.

Rectangle:

• Area of rectangle = lw
• Perimeter of rectangle = 2(l+w)

Here, l = length of rectangle and w = width of rectangle.

Parallelogram:

• Area of parallelogram = b × h
• Perimeter of parallelogram = 2(l+b)

Here, b = base of parallelogram and h = height of parallelogram.

Rhombus:

• Area of rhombus = (p × q) / 2
• Perimeter of rhombus = 4a

Here, p and q are the length of the diagonals and a is the side of rhombus.

Trapezium:

• Area = 1 / 2 h(a+b)
• Perimeter = Sum of all sides

Here a and b are the top and down sides of the trapezium. h is the height of the trapezium.

Triangle:

• Area of triangle = (1/2) x b x h

Here b and h are the base and height of the triangle respectively.

Regular Hexagon:

Circle:

• Circumference of a circle = 𝜋 x diameter
• Diameter of circle = 2r
• Area of a circle = 𝜋 x r x r

Here r is the radius of circle.

Cube:

Cuboid:

• Volume of a cuboid = (length × breadth × height) = lbh
• Total surface area of cuboid = 2(lb + bh + hl)

Cylinder:

• Area of curved surface = (perimeter of base) x height = 2𝜋rh
• Total surface area = 2𝜋r(r + h)
• Volume = 𝜋 x r x r x h

Cone:

• Curved surface area = 𝜋rl
• Total surface area = 𝜋r(r + l)
• Volume of cone = (1/3) x 𝜋 x r x r x h

Here l is the slant height of the cone.

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### Mensuration Tricks (क्षेत्रमिति ट्रिक्स)

 Mensuration Short Trick 1

If the length and the breadth of a rectangle are increased by x% and y% respectively, then the area of rectangle will increase by

Example: The length and breadth of a rectangle are increased by 20% and 40%, respectively. Find the percentage increase in its area.

Solution:

% increase in the area of rectangle

 Mensuration Short Trick 2

If the length of a rectangle is increased by x%, then its breadth will have to be decreased by

in order to maintain the same area of rectangle.

Example: The length of a rectangle is increased by 25%. By what per cent should its breadth be decreased so as to maintain the same area?

Solution:

The breadth must be decreased by

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 Mensuration Short Trick 3

If each of the defining dimensions or sides of any two-dimensional figure (triangle, rectangle, square, circle, quadrilateral, pentagon, hexagon, etc) is changed by x%, its area changes by

Example: If the radius of a circle is decreased by 10%, what is the percentage decrease in its area?

Solution:

∴ Area of the circle decreases by 19%

 Mensuration Short Trick 4

If r be the radius of a circle, then the area of a square inscribed in a circle is

Example: Find the area of a square inscribed in a circle of radius 10 cm.

Solution:

 Mensuration Short Trick 5

Area of the largest triangle inscribed in a semi-circle of radius r cm is

Example: Find the area of the largest triangle inscribed in semi-circle of radius 8 cm.

Solution: