Math / Geometry

QuestionFind the area of $\triangle W X Y$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth. $\square$ $m i^{2}$

Studdy Solution

STEP 1

What is this asking? We need to find the area of a triangle given the lengths of its three sides. Watch out! We can't just multiply the sides together!
We need a formula that relates the area of a triangle to its side lengths.

STEP 2

1. Calculate the semi-perimeter.
2. Apply Heron's formula.

STEP 3

Alright, first things first, we need the semi-perimeter, which is half the perimeter.
Let's call the sides $a$ , $b$ , and $c$ .
We have $a =$ 35 mi, $b =$ 36 mi, and $c =$ 29 mi.

STEP 4

The perimeter is just the sum of the sides: $a + b + c = 35 + 36 + 29 = \mathbf{100} \text{ mi}.$

STEP 5

Now, the semi-perimeter, which we'll call $s$ , is half of that: $s = \frac{100}{2} = \mathbf{50} \text{ mi}.$ So our semi-perimeter is 50 mi.

STEP 6

Now for the main event: Heron's formula!
It says the area of a triangle is $\sqrt{s(s-a)(s-b)(s-c)}.$ Remember, $s$ is the semi-perimeter, and $a$ , $b$ , and $c$ are the side lengths.

STEP 7

Let's plug in our values.
We have $s =$ 50, $a =$ 35, $b =$ 36, and $c =$ 29.
So we get: $\sqrt{50(50-35)(50-36)(50-29)}$ $= \sqrt{50 \cdot 15 \cdot 14 \cdot 21}$ $= \sqrt{220500}.$

STEP 8

Calculating the square root gives us approximately 469.57 mi $^2$ .
Rounding to the nearest tenth gives us 469.6 mi $^2$ .

STEP 9

The area of triangle WXY is approximately 469.6 mi $^2$ .

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QuestionFind the area of $\triangle W X Y$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth. $\square$ $m i^{2}$

Studdy Solution

STEP 1

What is this asking? We need to find the area of a triangle given the lengths of its three sides. Watch out! We can't just multiply the sides together!
We need a formula that relates the area of a triangle to its side lengths.

STEP 2

1. Calculate the semi-perimeter.
2. Apply Heron's formula.

STEP 3

Alright, first things first, we need the semi-perimeter, which is half the perimeter.
Let's call the sides $a$ , $b$ , and $c$ .
We have $a =$ 35 mi, $b =$ 36 mi, and $c =$ 29 mi.

STEP 4

The perimeter is just the sum of the sides: $a + b + c = 35 + 36 + 29 = \mathbf{100} \text{ mi}.$

STEP 5

Now, the semi-perimeter, which we'll call $s$ , is half of that: $s = \frac{100}{2} = \mathbf{50} \text{ mi}.$ So our semi-perimeter is 50 mi.

STEP 6

Now for the main event: Heron's formula!
It says the area of a triangle is $\sqrt{s(s-a)(s-b)(s-c)}.$ Remember, $s$ is the semi-perimeter, and $a$ , $b$ , and $c$ are the side lengths.

STEP 7

Let's plug in our values.
We have $s =$ 50, $a =$ 35, $b =$ 36, and $c =$ 29.
So we get: $\sqrt{50(50-35)(50-36)(50-29)}$ $= \sqrt{50 \cdot 15 \cdot 14 \cdot 21}$ $= \sqrt{220500}.$

STEP 8

Calculating the square root gives us approximately 469.57 mi $^2$ .
Rounding to the nearest tenth gives us 469.6 mi $^2$ .

STEP 9

The area of triangle WXY is approximately 469.6 mi $^2$ .

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QuestionFind the area of △WXY\triangle W X Y△WXY.Write your answer as an integer or as a decimal rounded to the nearest tenth. □\square□ mi2m i^{2}mi2

Studdy Solution

STEP 1

What is this asking? We need to find the area of a triangle given the lengths of its three sides. Watch out! We can't just multiply the sides together!We need a formula that relates the area of a triangle to its side lengths.

STEP 2

1. Calculate the semi-perimeter.2. Apply Heron's formula.

STEP 3

Alright, first things first, we need the **semi-perimeter**, which is half the perimeter.Let's call the sides aaa, bbb, and ccc.We have a=a = a= **35 mi**, b=b = b= **36 mi**, and c=c = c= **29 mi**.

STEP 4

The **perimeter** is just the sum of the sides: a+b+c=35+36+29=100 mi. a + b + c = 35 + 36 + 29 = \mathbf{100} \text{ mi}. a+b+c=35+36+29=100 mi.

STEP 5

Now, the **semi-perimeter**, which we'll call sss, is half of that: s=1002=50 mi. s = \frac{100}{2} = \mathbf{50} \text{ mi}. s=2100​=50 mi. So our **semi-perimeter** is **50 mi**.

STEP 6

Now for the main event: **Heron's formula**!It says the area of a triangle is s(s−a)(s−b)(s−c). \sqrt{s(s-a)(s-b)(s-c)}. s(s−a)(s−b)(s−c)​. Remember, sss is the **semi-perimeter**, and aaa, bbb, and ccc are the side lengths.

STEP 7

STEP 8

Calculating the square root gives us approximately **469.57 mi**2^22.Rounding to the nearest tenth gives us **469.6 mi**2^22.

STEP 9

The area of triangle WXY is approximately **469.6 mi**2^22.

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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.

QuestionFind the area of $\triangle W X Y$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth. $\square$ $m i^{2}$

What is this asking? We need to find the area of a triangle given the lengths of its three sides. Watch out! We can't just multiply the sides together!
We need a formula that relates the area of a triangle to its side lengths.

1. Calculate the semi-perimeter.
2. Apply Heron's formula.

Alright, first things first, we need the semi-perimeter, which is half the perimeter.
Let's call the sides $a$ , $b$ , and $c$ .
We have $a =$ 35 mi, $b =$ 36 mi, and $c =$ 29 mi.

The perimeter is just the sum of the sides: $a + b + c = 35 + 36 + 29 = \mathbf{100} \text{ mi}.$

Now, the semi-perimeter, which we'll call $s$ , is half of that: $s = \frac{100}{2} = \mathbf{50} \text{ mi}.$ So our semi-perimeter is 50 mi.

Now for the main event: Heron's formula!
It says the area of a triangle is $\sqrt{s(s-a)(s-b)(s-c)}.$ Remember, $s$ is the semi-perimeter, and $a$ , $b$ , and $c$ are the side lengths.

Calculating the square root gives us approximately 469.57 mi $^2$ .
Rounding to the nearest tenth gives us 469.6 mi $^2$ .

The area of triangle WXY is approximately 469.6 mi $^2$ .