Plane Geometry (Standard)

Multi-step exam-style items.

Phase 2 · ACT Math

Plane Geometry: core idea

a^2+b^2=c^2

A rhombus has diagonals $10$ and $16$ . Find its area.

Hint: Use half the product of diagonals. Answer: 80.

1. A circle's circumference is $18\pi$ . Find its area.
2. The exterior angle of a regular polygon is $45^\circ$ . Find its number of sides.
3. A $45$ - $45$ - $90$ triangle has leg $6$ . Find its hypotenuse.
4. A sector is $\frac13$ of a circle of radius $9$ . Find its area in terms of $\pi$ .
5. A rectangle has diagonal $13$ and width $5$ . Find its length.
6. The angles of a triangle are in ratio $2:3:4$ . Find the largest angle.
7. Find the area of a regular pentagon's interior-angle sum.
8. A circle has a chord $8$ units from its center and radius $10$ . Find half the chord length.
9. A regular hexagon has perimeter $42$ . Find its side length.