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Area from the Height

Part of the Triangles section of Coddy's Geometry journey. Lesson 52 of 60.

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 $\sqrt{{5}^{2}-{3}^{2}} = 4$ . Then the area is $\frac{1}{2}\cdot 6\cdot 4 = 12$ . 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

All lessons in Triangles

1The Triangle Inequality

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

4Area of a Triangle

Half the Rectangle Height Is Not a Side Right Triangle Area Finding the Height Any Side Can Be the Base Recap: Area

7Is It Right?

The Converse Testing a Triangle Acute or Obtuse?Sorting by the Test Recap: Right or Not

10Scale in the World

Shadows Across the River Nested Triangles A Side with an Expression Recap: Scale in the World

2Sides and Names

Sorting by Sides The Longest Side Ticks into Equations Recap: Sorting Triangles

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