Calculating Perimeter, Area, Volumes, and Angles of Basic Geometric Shapes

Introduction

In this section, we will learn how to calculate the perimeter, area, volumes, and angles of basic geometric shapes. Understanding these concepts is fundamental in geometry and will help you solve various mathematical problems.

Perimeter

The perimeter is the distance around a two-dimensional shape.

Rectangle Perimeter

The perimeter (P) of a rectangle is calculated using the formula:

$P = 2(l + w)$

where (l) is the length and (w) is the width.

Triangle Perimeter

The perimeter (P) of a triangle is the sum of the lengths of its sides:

$P = a + b + c$

where (a), (b), and (c) are the lengths of the sides.

Circle Perimeter

The perimeter (circumference) (C) of a circle is calculated using the formula:

$C = 2\pi r$

where (r) is the radius.

Area

The area is the amount of space inside a two-dimensional shape.

Rectangle Area

The area (A) of a rectangle is calculated using the formula:

$A = l \times w$

where (l) is the length and (w) is the width.

Triangle Area

The area (A) of a triangle is calculated using the formula:

$A = \frac{1}{2} \times b \times h$

where (b) is the base and (h) is the height.

Circle Area

The area (A) of a circle is calculated using the formula:

$A = \pi r^2$

where (r) is the radius.

Volume

The volume is the amount of space inside a three-dimensional shape.

Cube Volume

The volume (V) of a cube is calculated using the formula:

$V = s^3$

where (s) is the length of a side.

Rectangular Prism Volume

The volume (V) of a rectangular prism is calculated using the formula:

$V = l \times w \times h$

where (l) is the length, (w) is the width, and (h) is the height.

Cylinder Volume

The volume (V) of a cylinder is calculated using the formula:

$V = \pi r^2 h$

where (r) is the radius and (h) is the height.

Practice Problems

Calculate the perimeter of a rectangle with length 8 cm and width 5 cm.
Find the area of a triangle with base 10 cm and height 6 cm.
Determine the volume of a cube with side length 4 cm.
What is the circumference of a circle with radius 7 cm?

Practice Questions

Try some random questions to test your knowledge and understanding

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Rectangle Perimeter Triangle Area Cube Volume Circle Circumference

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