Math / Geometry

Question```latex \text{Find the perimeter of a composite shape that includes a semicircle with a diameter of } 7 \text{ ft.} ```

Studdy Solution

STEP 1

What is this asking? We need to find the total length around a shape that's like a half-circle! Watch out! Don't forget that perimeter includes both the curved part and the straight part of the semicircle.

STEP 2

1. Calculate the circumference of the full circle.
2. Calculate the circumference of the semicircle.
3. Calculate the total perimeter.

STEP 3

Alright, let's start by finding the circumference of the whole circle, even though we only have half of one.
The formula for the circumference of a circle is $C = 2 \cdot \pi \cdot r$ , where $C$ is the circumference and $r$ is the radius.

STEP 4

We're given the diameter, which is $7$ feet.
The radius is half the diameter, so $r = \frac{7}{2} = 3.5$ feet.

STEP 5

Now we can plug our radius into the circumference formula: $C = 2 \cdot \pi \cdot 3.5$ .

STEP 6

Let's calculate that! $C = 2 \cdot \pi \cdot 3.5 = 7\pi$ feet.
So, the circumference of the full circle is $7\pi$ feet.

STEP 7

Since we're dealing with a semicircle, we need half the circumference of the full circle.

STEP 8

Let's divide the full circumference by $2$ : $\frac{7\pi}{2}$ feet.
This is the length of the curved part of our semicircle.

STEP 9

Remember, the perimeter is the total distance around the shape.
We've got the curved part, which is $\frac{7\pi}{2}$ feet, but we also have the straight edge, which is the diameter of the semicircle!

STEP 10

We know the diameter is $7$ feet.
So, to get the total perimeter, we add the curved part and the diameter: $\frac{7\pi}{2} + 7$ feet.

STEP 11

The perimeter of the composite shape is $\frac{7\pi}{2} + 7$ feet.

Was this helpful?

Question```latex \text{Find the perimeter of a composite shape that includes a semicircle with a diameter of } 7 \text{ ft.} ```

Studdy Solution

STEP 1

What is this asking? We need to find the total length around a shape that's like a half-circle! Watch out! Don't forget that perimeter includes both the curved part and the straight part of the semicircle.

STEP 2

1. Calculate the circumference of the full circle.
2. Calculate the circumference of the semicircle.
3. Calculate the total perimeter.

STEP 3

Alright, let's start by finding the circumference of the whole circle, even though we only have half of one.
The formula for the circumference of a circle is $C = 2 \cdot \pi \cdot r$ , where $C$ is the circumference and $r$ is the radius.

STEP 4

We're given the diameter, which is $7$ feet.
The radius is half the diameter, so $r = \frac{7}{2} = 3.5$ feet.

STEP 5

Now we can plug our radius into the circumference formula: $C = 2 \cdot \pi \cdot 3.5$ .

STEP 6

Let's calculate that! $C = 2 \cdot \pi \cdot 3.5 = 7\pi$ feet.
So, the circumference of the full circle is $7\pi$ feet.

STEP 7

Since we're dealing with a semicircle, we need half the circumference of the full circle.

STEP 8

Let's divide the full circumference by $2$ : $\frac{7\pi}{2}$ feet.
This is the length of the curved part of our semicircle.

STEP 9

Remember, the perimeter is the total distance around the shape.
We've got the curved part, which is $\frac{7\pi}{2}$ feet, but we also have the straight edge, which is the diameter of the semicircle!

STEP 10

We know the diameter is $7$ feet.
So, to get the total perimeter, we add the curved part and the diameter: $\frac{7\pi}{2} + 7$ feet.

STEP 11

The perimeter of the composite shape is $\frac{7\pi}{2} + 7$ feet.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question```latex \text{Find the perimeter of a composite shape that includes a semicircle with a diameter of } 7 \text{ ft.} ```

Studdy Solution

STEP 1

What is this asking? We need to find the total length around a shape that's like a half-circle! Watch out! Don't forget that perimeter includes *both* the curved part *and* the straight part of the semicircle.

STEP 2

1. Calculate the circumference of the full circle.2. Calculate the circumference of the semicircle.3. Calculate the total perimeter.

STEP 3

Alright, let's **start** by finding the circumference of the *whole* circle, even though we only have half of one.The formula for the circumference of a circle is C=2⋅π⋅r C = 2 \cdot \pi \cdot r C=2⋅π⋅r, where C C C is the circumference and r r r is the radius.

STEP 4

We're given the **diameter**, which is 7 7 7 feet.The radius is *half* the diameter, so r=72=3.5 r = \frac{7}{2} = 3.5 r=27​=3.5 feet.

STEP 5

Now we can **plug** our radius into the circumference formula: C=2⋅π⋅3.5 C = 2 \cdot \pi \cdot 3.5 C=2⋅π⋅3.5.

STEP 6

Let's **calculate** that! C=2⋅π⋅3.5=7π C = 2 \cdot \pi \cdot 3.5 = 7\pi C=2⋅π⋅3.5=7π feet.So, the circumference of the *full* circle is 7π 7\pi 7π feet.

STEP 7

Since we're dealing with a *semi*circle, we need *half* the circumference of the full circle.

STEP 8

Let's **divide** the full circumference by 2 2 2: 7π2 \frac{7\pi}{2} 27π​ feet.This is the length of the curved part of our semicircle.

STEP 9

Remember, the perimeter is the total distance around the shape.We've got the curved part, which is 7π2 \frac{7\pi}{2} 27π​ feet, but we also have the straight edge, which is the **diameter** of the semicircle!

STEP 10

We know the diameter is 7 7 7 feet.So, to get the **total perimeter**, we **add** the curved part and the diameter: 7π2+7 \frac{7\pi}{2} + 7 27π​+7 feet.

STEP 11

The perimeter of the composite shape is 7π2+7 \frac{7\pi}{2} + 7 27π​+7 feet.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the total length around a shape that's like a half-circle! Watch out! Don't forget that perimeter includes both the curved part and the straight part of the semicircle.

1. Calculate the circumference of the full circle.
2. Calculate the circumference of the semicircle.
3. Calculate the total perimeter.

Alright, let's start by finding the circumference of the whole circle, even though we only have half of one.
The formula for the circumference of a circle is $C = 2 \cdot \pi \cdot r$ , where $C$ is the circumference and $r$ is the radius.

We're given the diameter, which is $7$ feet.
The radius is half the diameter, so $r = \frac{7}{2} = 3.5$ feet.

Now we can plug our radius into the circumference formula: $C = 2 \cdot \pi \cdot 3.5$ .

Let's calculate that! $C = 2 \cdot \pi \cdot 3.5 = 7\pi$ feet.
So, the circumference of the full circle is $7\pi$ feet.

Since we're dealing with a semicircle, we need half the circumference of the full circle.

Let's divide the full circumference by $2$ : $\frac{7\pi}{2}$ feet.
This is the length of the curved part of our semicircle.

Remember, the perimeter is the total distance around the shape.
We've got the curved part, which is $\frac{7\pi}{2}$ feet, but we also have the straight edge, which is the diameter of the semicircle!

We know the diameter is $7$ feet.
So, to get the total perimeter, we add the curved part and the diameter: $\frac{7\pi}{2} + 7$ feet.

The perimeter of the composite shape is $\frac{7\pi}{2} + 7$ feet.