Area from the Height

Part of the Triangles section of Coddy's Geometry journey. Lesson 63 of 71.

The area of a triangle is half the base times the height. When the height is a root expression, you can put it straight into the area formula and work everything out in one line. Take the isosceles triangle with equal sides 13 and base 10. Half the base is 5, so the height is √(13^2 - 5^2):

A = 1/2 × 10 × √(13^2 - 5^2)

A = 1/2 × 10 × √(144)

A = 1/2 × 10 × 12 = 60

Work from the inside out. First work out the squares under the root, then take the root, then multiply. The whole base, 10, is used in the area formula. Half the base, 5, is used only under the root to find the height.

Some problems do not give you the height or the side you need for the area or the perimeter. First use the Pythagorean theorem to find the missing length. Then put that length into the area or perimeter formula.