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]
3 years ago
10

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

Mathematics
1 answer:
MAVERICK [17]3 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
A farm lets you pick 3 pints of raspberries for 12.00 what is the price per pint/
BaLLatris [955]

Answer:

$4

Step-by-step explanation:

I tried to make it as simple as possible.

8 0
3 years ago
Read 2 more answers
The cost of 15 orange is Rs 75. How much price of 12 oranges​
stira [4]

1. The price of 3 metres of cloth is Rs 79.50. Find the price of 15 metres of such cloth. Solution: It is given that. Price of 3 m of cloth = Rs 79.50. We get. Price of 1 m of cloth = 79.50/3 = Rs 26.5. So the price of 15 m of cloth = 26.5 (15) = Rs 397.50. Hence, the price of 15 m of such cloth is Rs 397.50. 2. The cost of 17 chairs is Rs 9605.

Estimated Reading Time: 4 mins

4 0
2 years ago
Read 2 more answers
What is 531 x 321 x 345???
earnstyle [38]
The answer to that is 58,805,595 . hope this helps !!!
7 0
3 years ago
Read 2 more answers
X +2 times -2+107 = 180
Kryger [21]

Answer:

X = -3/7

Step-by-step explanation:

7 0
3 years ago
Four times a number is equal to the number increased by 15
valkas [14]

4x = x + 15

Hope this helps you! Hope your thanksgiving goes well, here's a turkey!

4 0
3 years ago
Other questions:
  • Could someone pkease help. i am not sure if i have the correct answer, thanks
    14·1 answer
  • Why do you need distributive property
    10·1 answer
  • Fraction is equivalent to a terminating decimal
    14·1 answer
  • adult tickets for the fall play cost $6 and students cost $3. the drama club so 25% more students tickets than adult tickets to
    12·1 answer
  • What place value is held by 3 in the number: 137,156
    7·1 answer
  • Scientific notation is ________.a. used to keep track of very small and very large numbers during mathematical calculations b. u
    11·1 answer
  • 5 STARS!!!
    14·1 answer
  • Casey surveyed the members of his soccer team to ask them what their favorite sport is
    6·1 answer
  • Which of these expressions or phrases can be used to represent the model choose all the correct answers
    9·1 answer
  • A ​30-inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third pie
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!