A right angle triangle has a base of √8 and a height of (√10+3). Show that the area is equal to 2√5+3√2.

The area of a triangle is equal to 1/2 x base x height, so we can write the equation for this question as: Area = 1/2 x √8 x (√10+3) We can then simplify √8 by writing it as its factors; √8 + √4√2, which equals 2√2. We can write it like this because 4 is a square number so its root is a rational number. We can the rewrite our area equation as: Area = 1/2 x 2√2 x (√10+3) and we can simplify it to Area = √2 x (√10+3) because 1/2 x 2√2 is just 2√2. We can now either expand the equation or play around with the numbers in the bracket to make things easier for ourselves. Lets look at √10. Using the same thing we did for √8, we can rewrite it as its factors; so √10 = √2√5. This will make our expansion much easier: √2 x (√2√5 +3) = √2√5 x √2 + 3 x√2 We can then simplify this complicated looking equation to get the answer we are looking for: Area = 2√5 + 3√2