Area Techniques (Hard)

Late AMC 10/12 through early AIME — dense computation.

Area Techniques: core idea

Ratio of areas.

A trapezoid has bases $10,18$ and area $140$ . Find height.

Hint: Select the formula matching the figure, and include all needed boundary pieces. Answer: 10.

1. Find the area of a regular hexagon of side $6$ .
2. A rhombus has diagonals $10,24$ . Find perimeter.
3. A radius- $12$ sector has angle $150^\circ$ . Find area.
4. Find the area of a $13$ - $14$ - $15$ triangle.
5. A square is inscribed in a radius- $5$ circle. Find its area.
6. A semicircle has area $18\pi$ . Find its perimeter.
7. Find the area between concentric circles of radii $5,13$ .
8. A parallelogram has sides $8,11$ and angle $30^\circ$ . Find area.
9. A rectangle's diagonal makes two triangles of area $45$ each. One side is $9$ . Find other side.