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Work out the area of triangle ABC.
(Surds)
Please help! I know how to find the area of a triangle but I get confused with how to do it with surds instead of numbers.
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Work out the area of triangle ABC Surds Please help I know how to find the area of a triangle but I get confused with how to do it with surds instead of numbers class=

Respuesta :

mhanifa

Answer:

  • 4 cm²

Step-by-step explanation:

Find the height BD using Pythagorean:

  • [tex]BD=\sqrt{AB^2-AD^2}[/tex]
  • [tex]BD= \sqrt{(2\sqrt{5})^2 -(3\sqrt{2})^2 } =\sqrt{20-18} =\sqrt{2}[/tex]

Find the base AC:

  • [tex]AC = AD + DC[/tex]
  • [tex]AC = 3\sqrt{2}+\sqrt{2}=4\sqrt{2}[/tex]

Find the area:

  • [tex]A = 1/2bh[/tex]
  • [tex]A = 1/2*AC*BD[/tex]
  • [tex]A=1/2*4\sqrt{2}*\sqrt{2} =4[/tex]

Answer:

  • 4 cm²

Step-by-step explanation:

We know that:

  • Area of triangle = 1/2 x Base x Altitude
  • Base = 3√2 + √2 = 4√2

Solution:

First, we need to find the altitude of the triangle. We can find the altitude using Pythagoras theorem.

  • => (2√5)² = (3√2)² + a²
  • => (2√5 x 2√5) = (3√2 x 3√2) + a²
  • => 20 = 18 + a²
  • => 20 - 18 = a²
  • => 2 = a²
  • => a = √2

Now, let's find the area of the triangle.

  • Area of triangle = 1/2 x Base x Altitude
  • => Area of triangle = 1/2 x 4√2 x √2
  • => Area of triangle = 1/2 x 4 x 2
  • => Area of triangle = 1/2 x 8
  • => Area of triangle = 4 cm²

Hence, the area of the triangle is 4 cm².

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