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natima [27]
3 years ago
11

Work out the area of triangle ABC.

Mathematics
1 answer:
AleksAgata [21]3 years ago
8 0

Answer:

A = 4 cm²

Step-by-step explanation:

The area of a triangle is calculated as

A = \frac{1}{2} bh ( b is the base and h the perpendicular height )

b = AC = 3\sqrt{2} + \sqrt{2} = 4\sqrt{2}

h = BD

Calculate BD using Pythagoras' identity in Δ ABD

BD² = AB² - AD²

      = (2\sqrt{5} )² - (3\sqrt{2} )²

     = 20 - 18 = 2 ( take square root of both sides )

BD = \sqrt{2}

Then

A = \frac{1}{2} × 4\sqrt{2} × \sqrt{2} = 2 × \sqrt{2} × \sqrt{2} = 4 cm²

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