SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Example

Title: Area of Square

Grade: 6-a Lesson: S1-L5

Explanation: The best way to understand geometry is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

A square field has a perimeter of 240 m. What is the length of its side and area?

Step 1a

The perimeter(P) of a square is P = \$4 times s\$

The given perimeter of a square is 240 m.

$1a$

Explanation: The perimeter of a square is calculated by multiplying the length of one of its sides by 4(p = 4s). If the given perimeter of a square is 240 m.

Step 1b

Solve for the side length(s):

Divide both sides of the equation by 4:

s = \$240 / 4\$

s = 60 meters

So, the length of each side of the square field is 60 meters.

Explanation: To determine the length (s) of each side of a square field. s = \$240/4\$. , First, divide 240 by 4, which gives you 60.Therefore, the length of each side of the square field is 60 meters.

Step 1c

Now, find the area of the square and use the formula for the area of a square: \$Area(A) = s^2\$

substitute the values A = \$(60)^2\$\$(60 times 60)\$ = 3600 sq.mtrs

Explanation: Now, let’s calculate the area of a square using the formula A = \$s^2\$, where A is the area and s is the length of one side. s = \$(60)^2\$ is 3600 sq.mtrs

Step 1d

Therefore, the area of a square is 3600 sq.meters.

Explanation: The area of a square is 3600 square meters.

The diagonal of a square is 20 units. Find the area & length of each side of the square.

Step 2a

In this case, let’s assume that each side of the square has a length of x units. Diagonal of a square is 20 units.

$2a$

Explanation: In this case, let’s assume that each side of the square has a length of x units. The diagonal of the square is 20 units.

Step 2b

Applying the Pythagorean theorem, we have: \$x^2 + x^2 = 20^2\$ = \$2x^2 = 400\$

Dividing both sides by 2, we have: \$x^2 = 200\$

Explanation: When applying the Pythagorean theorem to the equation \$x^2 + x^2 = 20^2\$, we can simplify it to

\$2x^2 = 400\$, and then to \$x^2\$ = 200.

Step 2c

Taking the square root of both sides, we find: x = \$\sqrt 200\$

Simplifying further, we have: x = \$\sqrt (100) \times 2\$ = \$10 \sqrt 2\$

Therefore, each side of a square is \$10 \sqrt 2\$ units.

Explanation:

Taking the square root of 200, we get x = \$10 \sqrt 2\$. Each side of a square measures 10 multiplied by the square root of 2 units.

Step 2d

Now, we have to find the area of a square Area = \$"side" times "side"\$ = \$10 \sqrt 2 times 10 \sqrt 2\$ = 200 sq.units

Hence, the area of a square is 200 sq.units

Explanation:

Let’s find the area of a square. The formula is \$"side" times "side"\$, which means in this case it’s \$10 \sqrt 2 times 10 \sqrt 2\$. Therefore, the area is 200 sq.units.