Calculate Rectangle Perimeter: Area = 45 Square Units

Q: Why can't I just add the area to the side lengths?

Area and perimeter measure different things! Area measures space inside (square units), while perimeter measures distance around (linear units). You must use the area to find the missing dimension first.

Q: How do I find the missing side when I know the area?

Use the area formula backwards! Since $ Area = length \times width $, you can find the missing side by dividing: $ width = \frac{Area}{length} = \frac{45}{9} = 5 $

Q: What's the difference between this rectangle and the explanation's rhombus?

The explanation incorrectly calls this a rhombus, but it's actually a rectangle! In rectangles, opposite sides are equal (like rhombuses), but all angles are 90°. The calculation method is the same.

Q: Do I need to memorize the perimeter formula?

The formula $ P = 2(length + width) $ helps, but you can also think: perimeter means going around the shape. Just add all four sides: length + width + length + width.

Q: How can I check if my perimeter is reasonable?

Your perimeter should be larger than any single side but much smaller than the area value. Here: perimeter = 28, which is greater than 9 or 5, and much less than area = 45. ✓

Rectangle Perimeter with Given Area

If the area of the rectangle below is equal to 45.

Calculate the perimeter of the rectangle.

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Understand the problem

If the area of the rectangle below is equal to 45.

Calculate the perimeter of the rectangle.

Step-by-step solution

Given that in a rhombus all opposite sides are parallel and equal to each other, we can state that:

$AC=DB=5$

$AB=CD=9$

Now let's calculate the perimeter by adding all sides together:

$5+9+5+9=10+18=28$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area = length × width for rectangles
Technique: Find missing dimension using $45 = 9 \times width$ , so width = 5
Check: Verify perimeter: 2(9 + 5) = 2(14) = 28 units ✓

Common Mistakes

Avoid these frequent errors

Adding area to the given dimensions
Don't calculate 45 + 9 + 5 = 59 as the perimeter! Area and perimeter are completely different measurements with different units. Always use the area to find the missing dimension first, then calculate perimeter using P = 2(length + width).

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why can't I just add the area to the side lengths?

Area and perimeter measure different things! Area measures space inside (square units), while perimeter measures distance around (linear units). You must use the area to find the missing dimension first.

How do I find the missing side when I know the area?

Use the area formula backwards! Since $Area = length \times width$ , you can find the missing side by dividing: $width = \frac{Area}{length} = \frac{45}{9} = 5$

What's the difference between this rectangle and the explanation's rhombus?

The explanation incorrectly calls this a rhombus, but it's actually a rectangle! In rectangles, opposite sides are equal (like rhombuses), but all angles are 90°. The calculation method is the same.

Do I need to memorize the perimeter formula?

The formula $P = 2(length + width)$ helps, but you can also think: perimeter means going around the shape. Just add all four sides: length + width + length + width.

How can I check if my perimeter is reasonable?

Your perimeter should be larger than any single side but much smaller than the area value. Here: perimeter = 28, which is greater than 9 or 5, and much less than area = 45. ✓

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