Everyday Math

Length and Area

Triangles - Calculating Area


What is the area of the right triangle above with side lengths 5,12,5, 12, and 1313?

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

In the above diagram, the area of ABD\triangle ABD is 2525 and the area of BCD\triangle BCD is 16.16. What is the ratio of the length of AD\overline{AD} to the length of DC?\overline{DC}?

In the above diagram, a=10,b=8,c=6,a=10, b=8, c=6, and CAB\angle CAB and AHB\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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