Unit 4 test: Geometry

What is the area of a triangle with side lengths $9$, $10$ and $17$?

Two sides of a triangle have lengths $6$ and $10$, and the angle between them measures $135^\circ$. What is the area of the triangle?

The altitude to the hypotenuse of a right triangle has length $6$ and cuts off a segment of length $3$ on the hypotenuse. How long is the hypotenuse?

The diagonals of a trapezoid with bases $5$ and $15$ meet at $P$. The triangle formed by $P$ and the shorter base has area $10$. What is the area of the trapezoid?

Chords $\overline{AB}$ and $\overline{CD}$ of a circle meet at $P$, with $AP = 2$, $PB = 12$ and $CD = 11$. What is the longer of $CP$ and $PD$?

Point $P$ is $13$ units from the center of a circle of radius $5$. A line through $P$ meets the circle at $A$ and $B$, with $A$ between $P$ and $B$ and $AB = 7$. What is $PA$?

In cyclic quadrilateral $ABCD$, $\angle BAC = 35^\circ$ and $\angle CAD = 45^\circ$. What is $\angle BCD$, in degrees?

Two secants from a point $P$ outside a circle intercept arcs of $130^\circ$ and $40^\circ$. What is the measure of the angle at $P$?

What is the area of the quadrilateral with vertices $(0, 0)$, $(8, 2)$, $(6, 7)$ and $(1, 5)$, in that order?

What is the distance from the point $(2, 3)$ to the line through $(0, -1)$ and $(4, 2)$?

What is the circumradius of a triangle with side lengths $5$, $7$ and $8$?

In $\triangle ABC$, $AB = 3$, $AC = 4$ and $\angle BAC = 60^\circ$. What is the length of the altitude from $A$ to $\overline{BC}$?

A rectangular box measures $2 \times 3 \times 6$. How long is the segment joining two opposite corners of the box?

A right circular cone has base radius $5$ and slant height $13$. What is its volume?

A regular tetrahedron has edge length $6$. What is the radius of the sphere that passes through all four of its vertices?