Math  /  Geometry

QuestionYou have been asked by your teacher to paint wooden arrows for the school's fair to help direct students on which direction to go. The dimensions of the wooden arrows are shown below.
What is the total area of the wooden figure that will be painted? 30 cm230 \mathrm{~cm}^{2} 54 cm254 \mathrm{~cm}^{2} 59 cm259 \mathrm{~cm}^{2} 74 cm274 \mathrm{~cm}^{2}
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Studdy Solution

STEP 1

What is this asking? We need to find the total area of a wooden arrow made up of a rectangle and a triangle. Watch out! Don't forget to add the area of *both* shapes!

STEP 2

1. Area of the rectangle
2. Area of the triangle
3. Total area

STEP 3

Alright class, let's **start** with the rectangle!
We know the area of a rectangle is length times width.
The **length** is 13 cm\text{13 cm} and the **width** is 3 cm\text{3 cm}.

STEP 4

So, we **multiply** those together: Arearectangle=lengthwidth=13 cm3 cm=39 cm2 \text{Area}_\text{rectangle} = \text{length} \cdot \text{width} = 13 \text{ cm} \cdot 3 \text{ cm} = 39 \text{ cm}^2 .
Boom! The **area of the rectangle** is 39 cm239 \text{ cm}^2.

STEP 5

Now, for the **triangle**!
The area of a triangle is one-half base times height.
We're given that the **base** is 10 cm\text{10 cm} and the **height** is 4 cm\text{4 cm}.

STEP 6

Let's **plug those values** into our formula: Areatriangle=12baseheight=1210 cm4 cm \text{Area}_\text{triangle} = \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 10 \text{ cm} \cdot 4 \text{ cm}.

STEP 7

Multiplying 1010 and 44 gives us 4040, and half of that is 2020.
So, the **area of the triangle** is 20 cm220 \text{ cm}^2.
Awesome!

STEP 8

Almost there!
To get the **total area**, we just need to **add** the area of the rectangle and the area of the triangle together.

STEP 9

We found that the **area of the rectangle** is 39 cm239 \text{ cm}^2 and the **area of the triangle** is 20 cm220 \text{ cm}^2.
So, the **total area** is 39 cm2+20 cm2=59 cm239 \text{ cm}^2 + 20 \text{ cm}^2 = 59 \text{ cm}^2.

STEP 10

The total area of the wooden arrow is 59 cm2\text{59 cm}^2.

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