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Math  /  Geometry

QuestionFind the area of the figure pictured below.
Area == □\square cm2\mathrm{cm}^{2}

Studdy Solution

STEP 1

What is this asking? We need to find out how much space this L-shaped figure takes up on a flat surface. Watch out! Don't forget to add the areas of both sections of the L-shape!
It's easy to miss one of them.

STEP 2

1. Break down the L-shape
2. Calculate the area of each rectangle
3. Add the areas together

STEP 3

Alright, let's start by **visualizing** this L-shaped figure as two separate rectangles.
Imagine cutting the L-shape into two rectangles: one vertical and one horizontal.
This makes it easier to handle!

STEP 4

The **vertical rectangle** is 11 cm tall and 3 cm wide.
The **horizontal rectangle** is 8 cm wide and 2 cm tall.
Got it?
Awesome!

STEP 5

Let's tackle the **vertical rectangle** first.
The formula for the area of a rectangle is **length times width**.
So, for the vertical rectangle, we have:
Area of vertical rectangle=11 cm⋅3 cm=33 cm2\text{Area of vertical rectangle} = 11 \, \text{cm} \cdot 3 \, \text{cm} = 33 \, \text{cm}^2

STEP 6

Now, let's move on to the **horizontal rectangle**.
Using the same formula, we get:
Area of horizontal rectangle=8 cm⋅2 cm=16 cm2\text{Area of horizontal rectangle} = 8 \, \text{cm} \cdot 2 \, \text{cm} = 16 \, \text{cm}^2

STEP 7

Finally, let's **combine** the areas of both rectangles to find the total area of the L-shaped figure.
So, we add them up:
Total Area=33 cm2+16 cm2=49 cm2\text{Total Area} = 33 \, \text{cm}^2 + 16 \, \text{cm}^2 = 49 \, \text{cm}^2

STEP 8

The area of the L-shaped figure is 49 cm2\boxed{49 \, \text{cm}^2}.

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