Question

Work out the area of triangle ABC.

Answer 1

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.

Answer 2

Answer:

• 4 cm²

Step-by-step explanation:

Find the height BD using Pythagorean:

• $BD=\sqrt{AB^2-AD^2}$
• $BD= \sqrt{(2\sqrt{5})^2 -(3\sqrt{2})^2 } =\sqrt{20-18} =\sqrt{2}$

Find the base AC:

• $AC = AD + DC$
• $AC = 3\sqrt{2}+\sqrt{2}=4\sqrt{2}$

Find the area:

• $A = 1/2bh$
• $A = 1/2*AC*BD$
• $A=1/2*4\sqrt{2}*\sqrt{2} =4$