Find the Rectangle Perimeter: When 4cm Square Equals 1cm-Sided Rectangle Area

Q: Why do I square the side length of 4 cm?

Because area of a square equals side × side. When the side is 4 cm, the area is $ 4^2 = 16 $ square cm. This is a fundamental area formula!

Q: How do I find the unknown side of the rectangle?

Since the areas are equal, set up the equation: square area = rectangle area. So $ 16 = 1 \times x $, which gives us $ x = 16 $ cm.

Q: What's the difference between area and perimeter?

Area measures the space inside (square units), while perimeter measures the distance around the outside (linear units). Here we use equal areas to find dimensions, then calculate perimeter.

Q: Why is the perimeter 34 and not 32?

The perimeter formula is $ 2 \times (length + width) = 2 \times (16 + 1) = 2 \times 17 = 34 $. Don't forget to multiply by 2 because rectangles have four sides!

Q: Can I check my answer?

Yes! Verify that both shapes have the same area: square = $ 4^2 = 16 $, rectangle = $ 16 \times 1 = 16 $. Then check perimeter: $ 16 + 1 + 16 + 1 = 34 $ ✓

Area Equivalence with Rectangle Perimeter

The area of the square whose side length is 4 cm is
equal to the area of the rectangle whose length of one of its sides is 1 cm.

What is the perimeter of the rectangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the rectangle

00:03 Apply the formula for calculating the area of a square

00:06 Side(4) squared

00:09 This is the area of the square

00:13 Apply the formula for calculating the area of a rectangle

00:16 Side(1) X side(X)

00:19 Substitute in the relevant values and solve for X

00:23 Now that we have the rectangle's sides, we can proceed to calculate its perimeter

00:26 The perimeter of the rectangle equals the sum of its sides

00:31 Substitute in the relevant values and solve for the perimeter

00:34 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the square whose side length is 4 cm is
equal to the area of the rectangle whose length of one of its sides is 1 cm.

What is the perimeter of the rectangle?

Step-by-step solution

After squaring all sides, we can calculate the area as follows:

$4^2=16$

Since we are given that the area of the square equals the area of the rectangle , we will write an equation with an unknown since we are only given one side length of the parallelogram:

$16=1\times x$

$x=16$

In other words, we now know that the length and width of the rectangle are 16 and 1, and we can calculate the perimeter of the rectangle as follows:

$1+16+1+16=32+2=34$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Square area = side², rectangle area = length × width
Technique: Set equal areas: 4² = 16 = 1 × x, so x = 16
Check: Perimeter = 2(length + width) = 2(16 + 1) = 34 ✓

Common Mistakes

Avoid these frequent errors

Calculating perimeter as length + width instead of full perimeter
Don't add just 16 + 1 = 17! This only gives you half the perimeter because rectangles have four sides. Always use the formula: perimeter = 2(length + width) = 2(16 + 1) = 34.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the rectangle below.

FAQ

Everything you need to know about this question

Why do I square the side length of 4 cm?

Because area of a square equals side × side. When the side is 4 cm, the area is $4^2 = 16$ square cm. This is a fundamental area formula!

How do I find the unknown side of the rectangle?

Since the areas are equal, set up the equation: square area = rectangle area. So $16 = 1 \times x$ , which gives us $x = 16$ cm.

What's the difference between area and perimeter?

Area measures the space inside (square units), while perimeter measures the distance around the outside (linear units). Here we use equal areas to find dimensions, then calculate perimeter.

Why is the perimeter 34 and not 32?

The perimeter formula is $2 \times (length + width) = 2 \times (16 + 1) = 2 \times 17 = 34$ . Don't forget to multiply by 2 because rectangles have four sides!

Can I check my answer?

Yes! Verify that both shapes have the same area: square = $4^2 = 16$ , rectangle = $16 \times 1 = 16$ . Then check perimeter: $16 + 1 + 16 + 1 = 34$ ✓

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Find the Rectangle Perimeter: When 4cm Square Equals 1cm-Sided Rectangle Area

Area Equivalence with Rectangle Perimeter

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I square the side length of 4 cm?

How do I find the unknown side of the rectangle?

What's the difference between area and perimeter?

Why is the perimeter 34 and not 32?

Can I check my answer?

🌟 Unlock Your Math Potential

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