SAT Geometry (Advanced)

Harder items at competition-adjacent depth.

Phase 2 · SAT Math

SAT Geometry: core idea

Similarity ratio scales length/area.

A right triangle has hypotenuse $25$ and one leg $7$ . Find the other leg.

Hint: Use $a^2+b^2=c^2$ . Answer: 24.

1. A cylinder has volume $200\pi$ and radius $5$ . Find its height.
2. A circle is inscribed in a square of side $14$ . Find the area inside the square but outside the circle.
3. In triangle $ABC$ , $DE\parallel BC$ , $AD=6$ , $DB=4$ , and $AE=9$ . Find $AC$ .
4. Find the area of a regular hexagon with side $4$ .
5. A sphere has radius $6$ . Find its surface area in terms of $\pi$ .
6. A triangle has sides $13,14,15$ . Find its area.
7. The endpoints of a diameter are $(2,3)$ and $(10,9)$ . Find the circle's radius.
8. A sector has radius $9$ and area $27\pi$ . Find its central angle.
9. A pyramid has square base side $6$ and height $10$ . Find its volume.