1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KATRIN_1 [288]
2 years ago
10

Find area of triangle formed by (1,1) (2,3) (4 ,5) using heron's formula ​

Mathematics
1 answer:
MAVERICK [17]2 years ago
7 0

Answer:

The area of a triangle is:

  • A = 1 unit²

Step-by-step explanation:

Given the points of a triangle

A(1, 1)

B(2, 3)

C(4, 5)

\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

Distance between AB:

AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}

     =\sqrt{1+4}

     =\sqrt{5}

so

  • a=\sqrt{5}

Distance between BC:

BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}

     =\sqrt{2^2+2^2}

     =\sqrt{2^3}

     =2\sqrt{2}

so

  • b=2\sqrt{2}

Distance between AC:

AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}

    =\sqrt{3^2+4^2}

   =\sqrt{5^2}

    =5

so

  • c=5

Semiperimeter = sum of sides ÷ 2            

                       s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224

Area of the triangle:

A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}

  • a=\sqrt{5}
  • b=2\sqrt{2}
  • c=5

A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}

A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}

A=1

Therefore, the area of a triangle is:

  • A = 1 unit²
You might be interested in
Caroline's car used 16 gallons to travel 544 miles. How far can she travel on 9 gallons?<br> ​
kicyunya [14]

Answer:

306 gallons

Step-by-step explanation:

Caroline traveled 544 miles on 16 gallons. We do some simple math and divide 544/16 and receive 34 miles/gallon. All we do now is multiply 34 * 9 and we receive 306 gallons.

8 0
2 years ago
List a pair of vertical angles, then state the relationship between vertical angles ​
strojnjashka [21]

Answer:

6, 8

7, 9

1, 4

they are congruent (same angle measure)

5 0
3 years ago
Read 2 more answers
What are the factors of xsquared+4x+3
Maslowich
The answer would be (x+1)(x+3)
4 0
3 years ago
Read 2 more answers
Write the following expression in decimal notation: 234 x 109.
Vikki [24]
234x10^9
=2.34x10^11
5 0
2 years ago
2280÷60 how to work it out
Arturiano [62]
You could do 228/6 = 38 

2280/60 = 38

hope this helps you
4 0
3 years ago
Other questions:
  • People arrive at a college admissions office at rate 1 per minute, and the arrival is a Poisson process. When k people have arri
    6·1 answer
  • 5(x - 3) = 7x 2 Step 1 ⇒ 10(x - 3) = 7x Step 2 ⇒ 10x - 30 = 7x Step 3 ⇒ 3x - 30 = 0 Step 4 ⇒ 3x = 30 Step 5 ⇒ x = 10 Identify th
    7·2 answers
  • Which of the following represents the zeros of f(x) = 6x^3-31x^2+4x+5
    7·2 answers
  • How many hundreds does 4 thousands equal
    15·1 answer
  • Which word phrases is correct? 0.223 two hundred twenty-three hundredths two hundred twenty-three thousandths
    7·2 answers
  • What is the best first step to solve the inequality 5x - 322?
    13·1 answer
  • Determine which of the following situations models a unit rate of $0.75. Select all situations that apply.
    14·1 answer
  • Please help I will give 25points
    7·2 answers
  • What is twice the larger root of x^2-9x+3=0
    9·1 answer
  • Write each phrase as a mathematical expression.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!