Area Techniques (Medium)

AMC 10/12 mid (≈Q9–16) — multi-step.

Area Techniques: core idea

Heron mid.

A circle has diameter $10$ . Find its area in terms of $\pi$ .

Hint: Break composite figures into familiar pieces. Answer: 25\pi.

1. Find the area of a rhombus with diagonals $8$ and $12$ .
2. A triangle has sides $3,4,5$ . Find its area.
3. Find the area of a regular hexagon made of six equilateral triangles of side $2$ .
4. A square has diagonal $10$ . Find its area.
5. Find the area of an annulus with outer radius $5$ and inner radius $3$ .
6. A trapezoid has area $36$ , bases $6,12$ . Find its height.
7. A rectangle has perimeter $30$ and one side $6$ . Find its area.
8. Find the area of a sector of $90^\circ$ in a circle of radius $6$ .
9. A triangle has area $24$ and base $8$ . Find its height.