Geometry

Properties of Triangles

Triangles - Calculating Area

What is the area of the right triangle above with side lengths 5 , 12 , 5, 12, and 13 13 ?

In triangle A B C ABC above, the lengths of some line segments are as follows: B H = 3 , C H = 2 , A H = 4. \begin{array}{c}&BH=3, &CH=2, &AH=4. \end{array} What is the ratio of the area of A B H \triangle ABH to the area of A C H ? \triangle ACH?

In the above diagram, the area of A B D \triangle ABD is 25 25 and the area of B C D \triangle BCD is 16. 16. What is the ratio of the length of A D \overline{AD} to the length of D C ? \overline{DC}?

In the above diagram, a = 10 , b = 8 , c = 6 , a=10, b=8, c=6, and C A B \angle CAB and A H B \angle AHB are right angles. Find the value of x . x.

Hint: Find two different ways to represent the area (one using the legs and one using the hypotenuse) and set them equal.

What is the area of a triangle with side lengths 18, 24, and 30?

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