Math / Geometry

QuestionUse Heron's formula to find the area of the triangle. Round to the nearest square foot. Side $a=8$ feet Side $b=8$ feet Side $c=4$ feet
The area is approximately $\square$ square feet.

Studdy Solution

STEP 1

What is this asking? We need to find the area of a triangle given the lengths of its three sides, and we're going to use Heron's awesome formula to do it! Watch out! Don't forget to find the semi-perimeter first before plugging values into Heron's formula.
Also, remember to round to the nearest square foot at the end.

STEP 2

1. Calculate the semi-perimeter
2. Apply Heron's Formula
3. Round to the nearest square foot

STEP 3

The semi-perimeter, often denoted by $s$ , is half the sum of the lengths of all three sides of the triangle.
It's like finding the perimeter and then cutting it in half!
We have side $a = 8$ feet, side $b = 8$ feet, and side $c = 4$ feet.

STEP 4

Let's add all the side lengths together: $8 + 8 + 4 = 20$ feet.
This is the perimeter.
Now, we divide this by $2$ to get the semi-perimeter: $s = \frac{20}{2} = 10$ feet.
So, our semi-perimeter $s$ is 10 feet!

STEP 5

Heron's formula is a super cool way to find the area of a triangle when you know the lengths of all three sides.
The formula is: $\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$ where $s$ is the semi-perimeter, and $a$ , $b$ , and $c$ are the lengths of the sides.

STEP 6

We already found that $s = 10$ feet.
Now, let's plug in all the values: $\text{Area} = \sqrt{10(10-8)(10-8)(10-4)}$

STEP 7

Let's simplify inside the parentheses: $\text{Area} = \sqrt{10 \cdot 2 \cdot 2 \cdot 6}$

STEP 8

Now, let's multiply those numbers together: $\text{Area} = \sqrt{240}$

STEP 9

Finally, let's calculate the square root: $\text{Area} \approx 15.49193338$

STEP 10

We found that the area is approximately $15.49193338$ square feet.
Since we need to round to the nearest square foot, we look at the digit after the decimal point.
It's a $4$ , which is less than $5$ , so we round down.

STEP 11

Our final answer is approximately $15$ square feet.

STEP 12

The area of the triangle is approximately $15$ square feet.

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QuestionUse Heron's formula to find the area of the triangle. Round to the nearest square foot. Side $a=8$ feet Side $b=8$ feet Side $c=4$ feet
The area is approximately $\square$ square feet.

Studdy Solution

STEP 1

STEP 2

1. Calculate the semi-perimeter
2. Apply Heron's Formula
3. Round to the nearest square foot

STEP 3

The semi-perimeter, often denoted by $s$ , is half the sum of the lengths of all three sides of the triangle.
It's like finding the perimeter and then cutting it in half!
We have side $a = 8$ feet, side $b = 8$ feet, and side $c = 4$ feet.

STEP 4

Let's add all the side lengths together: $8 + 8 + 4 = 20$ feet.
This is the perimeter.
Now, we divide this by $2$ to get the semi-perimeter: $s = \frac{20}{2} = 10$ feet.
So, our semi-perimeter $s$ is 10 feet!

STEP 5

Heron's formula is a super cool way to find the area of a triangle when you know the lengths of all three sides.
The formula is: $\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$ where $s$ is the semi-perimeter, and $a$ , $b$ , and $c$ are the lengths of the sides.

STEP 6

We already found that $s = 10$ feet.
Now, let's plug in all the values: $\text{Area} = \sqrt{10(10-8)(10-8)(10-4)}$

STEP 7

Let's simplify inside the parentheses: $\text{Area} = \sqrt{10 \cdot 2 \cdot 2 \cdot 6}$

STEP 8

Now, let's multiply those numbers together: $\text{Area} = \sqrt{240}$

STEP 9

Finally, let's calculate the square root: $\text{Area} \approx 15.49193338$

STEP 10

We found that the area is approximately $15.49193338$ square feet.
Since we need to round to the nearest square foot, we look at the digit after the decimal point.
It's a $4$ , which is less than $5$ , so we round down.

STEP 11

Our final answer is approximately $15$ square feet.

STEP 12

The area of the triangle is approximately $15$ square feet.

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QuestionUse Heron's formula to find the area of the triangle. Round to the nearest square foot. Side a=8a=8a=8 feet Side b=8b=8b=8 feet Side c=4c=4c=4 feetThe area is approximately □\square□ square feet.

Studdy Solution

STEP 1

STEP 2

1. Calculate the semi-perimeter2. Apply Heron's Formula3. Round to the nearest square foot

STEP 3

The **semi-perimeter**, often denoted by sss, is half the sum of the lengths of all three sides of the triangle.It's like finding the perimeter and then cutting it in half!We have side a=8a = 8a=8 feet, side b=8b = 8b=8 feet, and side c=4c = 4c=4 feet.

STEP 4

Let's **add** all the side lengths together: 8+8+4=208 + 8 + 4 = 208+8+4=20 feet.This is the **perimeter**.Now, we **divide** this by 222 to get the **semi-perimeter**: s=202=10s = \frac{20}{2} = 10s=220​=10 feet.So, our **semi-perimeter** sss is **10** feet!

STEP 5

STEP 6

We already found that s=10s = 10s=10 feet.Now, let's **plug in** all the values: Area=10(10−8)(10−8)(10−4) \text{Area} = \sqrt{10(10-8)(10-8)(10-4)} Area=10(10−8)(10−8)(10−4)​

STEP 7

Let's **simplify** inside the parentheses: Area=10⋅2⋅2⋅6 \text{Area} = \sqrt{10 \cdot 2 \cdot 2 \cdot 6} Area=10⋅2⋅2⋅6​

STEP 8

Now, let's **multiply** those numbers together: Area=240 \text{Area} = \sqrt{240} Area=240​

STEP 9

Finally, let's **calculate** the square root: Area≈15.49193338 \text{Area} \approx 15.49193338 Area≈15.49193338

STEP 10

We found that the area is approximately 15.4919333815.4919333815.49193338 square feet.Since we need to round to the nearest square foot, we look at the digit after the decimal point.It's a 444, which is less than 555, so we round *down*.

STEP 11

Our **final answer** is approximately 151515 square feet.

STEP 12

The area of the triangle is approximately 151515 square feet.

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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.

QuestionUse Heron's formula to find the area of the triangle. Round to the nearest square foot. Side $a=8$ feet Side $b=8$ feet Side $c=4$ feet
The area is approximately $\square$ square feet.

1. Calculate the semi-perimeter
2. Apply Heron's Formula
3. Round to the nearest square foot

The semi-perimeter, often denoted by $s$ , is half the sum of the lengths of all three sides of the triangle.
It's like finding the perimeter and then cutting it in half!
We have side $a = 8$ feet, side $b = 8$ feet, and side $c = 4$ feet.

Let's add all the side lengths together: $8 + 8 + 4 = 20$ feet.
This is the perimeter.
Now, we divide this by $2$ to get the semi-perimeter: $s = \frac{20}{2} = 10$ feet.
So, our semi-perimeter $s$ is 10 feet!

We already found that $s = 10$ feet.
Now, let's plug in all the values: $\text{Area} = \sqrt{10(10-8)(10-8)(10-4)}$

Let's simplify inside the parentheses: $\text{Area} = \sqrt{10 \cdot 2 \cdot 2 \cdot 6}$

Now, let's multiply those numbers together: $\text{Area} = \sqrt{240}$

Finally, let's calculate the square root: $\text{Area} \approx 15.49193338$

We found that the area is approximately $15.49193338$ square feet.
Since we need to round to the nearest square foot, we look at the digit after the decimal point.
It's a $4$ , which is less than $5$ , so we round down.

Our final answer is approximately $15$ square feet.

The area of the triangle is approximately $15$ square feet.