Respuesta :

calculista

see the attached figure to better understand the problem

we know that

the area of the triangle ABC is equal to the area of the triangle 1

The area of the triangle 1,2,3 and 4 is the area of a rectangle

The area of the rectangle is equal to

[tex]A=3*5=15\ units^{2}[/tex]

Find the area of the triangle 2

[tex]A2=\frac{1}{2}*(2*4)=4\ units^{2}[/tex]

Find the area of the triangle 3

[tex]A2=\frac{1}{2}*(1*5)=\frac{5}{2}\ units^{2}[/tex]

Find the area of the triangle 4

[tex]A2=\frac{1}{2}*(3*1)=\frac{3}{2}\ units^{2}[/tex]

Find the area of the triangle ABC

[tex]A1=15\ units^{2}-(4\ units^{2}+\frac{5}{2}\ units^{2}+\frac{3}{2}\ units^{2})\\ \\A1=15\ units^{2}-(8\ units^{2})\\ \\ A1=7\ units^{2}[/tex]

therefore

the answer is

the area of the triangle ABC is equal to

[tex]7\ units^{2}[/tex]


Ver imagen calculista
BladeRunner212

7 square units

Further explanation

Let us find out the area of ​​triangle ABC using an alternative method.

We divide the triangle ABC into three triangles, which are:

  • AOC triangle as a right triangle
  • AOB triangle as an obtuse triangle
  • BOC triangle as an obtuse triangle

We prepare the base and height of each triangle.

ΔAOC

  • Base = 2 units
  • Height = 4 units

ΔAOB

  • Base = 2 units
  • Height = 1 units

ΔBOC

  • Base = 4 units
  • Height = 1 units

To recall the base and height of an obtuse triangle, look at the attached picture.

The formula of area of triangle is [tex]\boxed{ \ Area = \frac{1}{2} \times base \times height \ }[/tex]

Let us calculate the area of each triangle.

The area of triangle AOC = [tex]\boxed{ \ \frac{1}{2} \times 2 \times 4 = 4 \ square \ units \ }[/tex]

The area of triangle AOB = [tex]\boxed{ \ \frac{1}{2} \times 2 \times 1 = 1 \ square \ units \ }[/tex]

The area of triangle BOC = [tex]\boxed{ \ \frac{1}{2} \times 4 \times 1 = 2 \ square \ units \ }[/tex]

And now, let us find out the area of triangle ABC.

The area of ΔABC = the area of ΔAOC + the area of ΔAOB + the area of ΔBOC

The area of ΔABC = 4 + 1 + 2

The area of ΔABC = 7

Thus, the area of triangle ABC is 7 square units.

Learn more

  1. Find out the measures of the two angles in a right triangle https://brainly.com/question/4302397
  2. Find out the area of a parallelogram https://brainly.com/question/4459688
  3. Find out the area of a cube  https://brainly.com/question/12613605#

Keywords: what, the area of triangle ABC, right, obtuse, base, height, formula, alternative method

Ver imagen BladeRunner212

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