Area from the Height

Part of the Triangles section of Coddy's Geometry journey. Lesson 55 of 63.

An area question often hides a Pythagoras question. The area needs a height, and if the figure gives only the sides, you find the height first.

$Isosceles triangle with equal sides 5 and base 6$

Here the equal sides are 5 and the base is 6. Half the base is 3, so the height is √(5^2 - 3^2) = 4. Then the area is 1/2 × 6 × 4 = 12. Three steps on the stage: Midpoint, Pythagorean theorem, Area of a triangle.

Challenge

△ABC is isosceles with AB = AC = 17 and base BC = 16. Its height AD is drawn but not labelled. Find the area of △ABC, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles

2The Triangle Inequality

Can Three Sticks Meet?Exactly Reaching The Range of the Third Side The Formula Recap: The Third Side

5The Pythagorean Theorem

Squares on the Sides Finding the Hypotenuse Pythagorean Triples When It Is Not Whole Recap: The Hypotenuse

8Special Right Triangles

The 45-45-90 Triangle Legs from the Hypotenuse The 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an IsoscelesArea from the HeightThe Equilateral Triangle Right Triangle Perimeter Recap: Two Tools