Geometry
Area of Triangles
Which has the greater area:
A: A square with side lengths of \(x.\)
B. A triangle with base length \(x\) that is twice as tall as it is wide.
Shayna draws triangle \(P\) with a base and a height greater than one. She triples the base length and halves the height to get triangle \(Q.\) Which triangle has greater area?
One way to find the area of a triangle is to use the Sine Rule: Area = \(\frac{1}{2}ab \sin{C}.\) In the formula, \( a \) and \( b \) are the adjacent sides to any angle angle \( C \) of the triangle.
If \(\text {sin }\angle HUT\) is \(\frac{1}{2},\) what is the area of \(\triangle HUT?\)