Formula for Area – Essential Formulas You Should Know

Introduction:

The area formula is essential for finding the number of square units enclosed by a polygon. This article provides a comprehensive overview of frequently used area formulas for various shapes such as squares, rectangles, circles, triangles, parallelograms, rhombuses, trapezoids, and ellipses. It also includes examples to help readers understand how to apply these formulas in real-life scenarios.

Full Article: Formula for Area – Essential Formulas You Should Know

Discover the Area Formulas for Different Shapes

Understanding the area formula is crucial when it comes to calculating the space enclosed by different shapes. Whether you’re a student or just curious about mathematics, these frequently used area formulas will help you grasp the concept and apply it to real-world scenarios. Let’s dive in!


Area of a Square

Consider a square with equal sides. The area of the square is obtained by squaring the length of one side, represented by variable ‘s’.

Formula: A = s2 = s × s


Area of a Rectangle

For a rectangle, its area is found by multiplying its base (‘b’) and height (‘h’). It can also be calculated using the formula A = length × width.

Formula: A = b × h = bh


Area of a Circle

The area of a circle is determined by multiplying pi (‘π’) and the square of its radius (‘r’).

Formula: A = πr2


Area of a Triangle

Consider a triangle with base (‘b’) and height (‘h’). Its area can be found by multiplying the base and height, then dividing the product by 2.

Formula: Area = (b × h) / 2


Area of a Parallelogram

When calculating the area of a parallelogram, simply multiply its base (‘b’) and height (‘h’).

Formula: A = b × h = bh


Area of a Rhombus

A rhombus (or kite) has an area equal to half the product of the lengths of its diagonals (‘d1‘ and ‘d2‘).

Formula: A = (d1 × d2) / 2


Area of a Trapezoid

For a trapezoid, the area is half the product of its height (‘h’) and the sum of its bases (‘b1‘ and ‘b2‘).

Formula: A = [h(b1 + b2)] / 2


Area of an Ellipse

An ellipse’s area is calculated by multiplying pi (‘π’) with the length of its semi-major axis (‘a’) and semi-minor axis (‘b’).

Formula: A = πab


Example: Area of a Rectangular Backyard

Problem: Find the area of a rectangular backyard with dimensions 50 feet (length) and 40 feet (breadth).

Solution:

Length of the backyard = 50 ft
Breadth of the backyard = 40 ft

Area of the backyard = length × breadth

Area = 50 ft × 40 ft

Area = 2,000 square feet (2000 ft2)


Example: Area of a Parallelogram

Problem: In a parallelogram, given one base of 12 cm, height of 6 cm, and an area of 72 cm2, find the height corresponding to the other base of 15 cm.

Solution:

Area = base × height

Area = 12 × 6 = 72 cm2

Since the area remains the same, use the formula to find the height corresponding to the 15 cm base.

72 = 15 × height

height = 72 / 15 = 4.8 cm

The height corresponding to the 15 cm base is 4.8 cm.


Example: Area of a Circle

Problem: Calculate the area of a circle with a diameter of 9 units.

Solution:

Radius = Diameter / 2 = 9 / 2 = 4.5 units

Area = π × (radius)2

Area = 3.14 × (4.5)2

Area ≈ 63.585 square units

Summary: Formula for Area – Essential Formulas You Should Know

The article discusses various area formulas for different shapes such as squares, rectangles, circles, triangles, parallelograms, rhombuses, trapezoids, and ellipses. It provides examples on how to use these formulas to calculate the area of different figures. This article is informative and easy to understand for readers seeking knowledge about area formulas.




FAQs – Area Formula


Frequently Asked Questions

Question 1: What is the area formula for a rectangle?

Answer: The area formula for a rectangle is given by multiplying the length of the rectangle by its width: A = length × width.

Question 2: What is the area formula for a square?

Answer: The area formula for a square is simply the length of one side squared: A = side × side or A = side^2.

Question 3: How do you calculate the area of a triangle?

Answer: To calculate the area of a triangle, multiply the base of the triangle by its height and divide the result by 2: A = (base × height) / 2.

Question 4: What is the formula for the area of a circle?

Answer: The formula for the area of a circle is given by multiplying π (pi) by the radius of the circle squared: A = πr^2.

Question 5: How can I find the area of a trapezoid?

Answer: To find the area of a trapezoid, multiply the sum of its two parallel sides (a and b) by its height (h) and divide the result by 2: A = ((a + b) × h) / 2.

Question 6: What is the area formula for a parallelogram?

Answer: The area of a parallelogram is given by multiplying its base (b) by its height (h): A = b × h.

Question 7: What is the area formula for a rhombus?

Answer: The area of a rhombus can be calculated by multiplying the lengths of its diagonals and dividing the result by 2: A = (d1 × d2) / 2, where d1 and d2 are the lengths of the diagonals.

Question 8: How do you find the area of a regular polygon?

Answer: The area of a regular polygon can be found by multiplying the apothem (the distance between the center and any side) by the perimeter of the polygon and dividing the result by 2: A = (apothem × perimeter) / 2.

Question 9: What is the formula for the area of an ellipse?

Answer: The formula for the area of an ellipse is given by multiplying π (pi) by the lengths of its semi-major axis (a) and semi-minor axis (b): A = πab.

Question 10: How do you calculate the area of a sector in a circle?

Answer: To find the area of a sector in a circle, multiply the central angle (in radians) by half the square of the radius: A = (θr^2) / 2, where θ is the central angle.

Question 11: What is the area formula for a regular hexagon?

Answer: The area of a regular hexagon can be found by multiplying 3 times the square of its side length (s) by the square root of 3 divided by 2: A = (3s^2 √3) / 2.

Question 12: How can I calculate the area of a cylinder?

Answer: To find the area of a cylinder, sum the areas of its two bases (circles) and the lateral surface area (rectangle) given by the product of the height (h) and the perimeter of the base: A = 2πr^2 + 2πrh.

Question 13: What is the area formula for a cone?

Answer: The formula for the area of a cone includes the curved surface area and the area of the base. The curved surface area (lateral area) is given by πrℓ, and the base area is πr^2, where r is the radius and ℓ is the slant height.

Question 14: How do you calculate the area of a sphere?

Answer: The area of a sphere is given by multiplying 4 times π (pi) by the radius squared: A = 4πr^2.

Question 15: What is the area formula for a sector in a circle?

Answer: To calculate the area of a sector in a circle, multiply the central angle (in degrees) by π (pi) and the square of the radius, and divide the result by 360: A = (θπr^2) / 360.

Question 16: How do you find the area of a composite figure?

Answer: To find the area of a composite figure, separate it into smaller, familiar shapes (e.g., triangles, rectangles, circles), calculate the area of each individual shape, and then sum their areas.

Question 17: What is the formula for the area of an irregular polygon?

Answer: The area of an irregular polygon can be determined by dividing it into smaller triangles/rectangles, calculating their individual areas, and summing them to obtain the total area.

Question 18: How do you find the area of a pentagon?

Answer: The area of a regular pentagon with side length (s) can be computed using the formula A = (5s^2) / (4tan(π/5)), where tan(π/5) is the tangent of 36 degrees.

Question 19: What is the formula for the area of an equilateral triangle?

Answer: The formula for the area of an equilateral triangle with side length (s) is given by A = (s^2√3)/4 or A = (s^2√3)/3, depending on the convention used.

Question 20: How can I find the area of a hemisphere?

Answer: The area of a hemisphere can be calculated by summing the areas of its curved surface area (given by 2πr^2) and the area of its base (a circle with radius r).



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