Calculate the Area of a Rectangle: Two 5-Unit Squares Combined

Q: Why can I solve this problem in two different ways?

Because the rectangle is made of two identical squares! You can either treat it as one rectangle (10 × 5) or as two separate squares (25 + 25). Both methods give the same answer: 50.

Q: How do I know the length is 10 if it's not labeled?

Look at the diagram carefully! The rectangle is made of two 5-unit squares placed side by side. So the total length is 5 + 5 = 10 units, while the width stays 5 units.

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

Area measures the space inside a shape (multiply length × width). Perimeter measures the distance around a shape (add all the sides). For this rectangle: Area = 50, Perimeter = 30.

Rectangle Area with Combined Squares

Look at the given rectangle made of two squares below:

What is its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the area of the rectangle AFCD

00:03 In a square all sides are equal

00:15 To calculate the area of the rectangle, we must calculate the areas of the squares

00:23 To calculate the area of a square, multiply side(5) by side(5)

00:27 This is the area of the squares

00:36 Add up the areas of the squares to determine the area of the rectangle

00:41 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the given rectangle made of two squares below:

What is its area?

Step-by-step solution

In a square all sides are equal, therefore we know that:

$AB=BC=CD=DE=EF=FA=5$

The area of the rectangle can be found in two ways:

Find one of the sides (for example AC)
$AC=AB+BC$
$AC=5+5=10$
and multiply it by one of the adjacent sides to it (CD/FA, which we already verified is equal to 5)
$5\times10=50$
Find the area of the two squares and add them.
The area of square BCDE is equal to the multiplication of two adjacent sides, both equal to 5.
$5\times5=25$
Square BCDE is equal to square ABFE, because their sides are equal and they are congruent.
Therefore, the sum of the two squares is equal to:
$25+25=50$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Formula: Area equals length times width (A = l × w)
Method: Calculate as 10 × 5 = 50 or add two squares: 25 + 25 = 50
Verify: Both squares have area 25, so total rectangle area is 50 ✓

Common Mistakes

Avoid these frequent errors

Calculating area as perimeter
Don't add all the sides like 5 + 5 + 5 + 5 + 5 + 5 = 30! This gives you the perimeter, not the area. Perimeter measures distance around the shape, while area measures space inside. Always multiply length × width for rectangle area.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why can I solve this problem in two different ways?

Because the rectangle is made of two identical squares! You can either treat it as one rectangle (10 × 5) or as two separate squares (25 + 25). Both methods give the same answer: 50.

How do I know the length is 10 if it's not labeled?

Look at the diagram carefully! The rectangle is made of two 5-unit squares placed side by side. So the total length is 5 + 5 = 10 units, while the width stays 5 units.

What's the difference between area and perimeter?

Area measures the space inside a shape (multiply length × width). Perimeter measures the distance around a shape (add all the sides). For this rectangle: Area = 50, Perimeter = 30.

Can I just count the unit squares in the diagram?

Yes! Each small square would be 1 × 1 = 1 unit. Since each side of our squares is 5 units, each square contains $5 \times 5 = 25$ unit squares. Two squares = 50 unit squares total.

What if the squares were different sizes?

Then you'd need to find the area of each square separately and add them together. But in this problem, both squares are identical with sides of 5 units each.

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