ACT · Mathematics

Geometry and trigonometry

25 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 25 questions

A triangle has a base of $14$ and a height of $11$ . What is its area?
A triangle has a base of $10$ and a height of $3$ . What is its area?
A triangle has a base of $16$ and a height of $5$ . What is its area?
A triangle has a base of $16$ and a height of $7$ . What is its area?
A right triangle has legs of length $20$ and $21$ . What is the length of its hypotenuse?
A triangle has a base of $10$ and a height of $7$ . What is its area?
A triangle has a base of $12$ and a height of $11$ . What is its area?
A triangle has a base of $14$ and a height of $7$ . What is its area?
A triangle has a base of $10$ and a height of $9$ . What is its area?
A triangle has a base of $6$ and a height of $7$ . What is its area?
A triangle has a base of $8$ and a height of $11$ . What is its area?
In a circle of radius $10$ , two parallel chords have lengths $16$ and $12$ . The chords lie on opposite sides of the center. What is the distance between the chords?
Angle $θ$ is in Quadrant II and $sin θ = \frac{3}{5}$ . What is $tan 2 θ$ ?
In triangle $A B C$ , $A B = 7$ , $A C = 9$ and $∠ A = 6 0^{\circ}$ . What is the length of $B C$ ?
A right triangle has legs of length $5$ and $12$ . What is the length of its hypotenuse?
A right triangle has legs of length $8$ and $15$ . What is the length of its hypotenuse?
A right triangle has legs of length $7$ and $24$ . What is the length of its hypotenuse?
A right triangle has legs of length $9$ and $12$ . What is the length of its hypotenuse?
A right triangle has legs of length $12$ and $16$ . What is the length of its hypotenuse?
A triangle has a base of $10$ and a height of $11$ . What is its area?
A triangle has a base of $12$ and a height of $5$ . What is its area?
A right triangle has legs of length $9$ and $12$ . What is the length of the altitude drawn to the hypotenuse?
In a circle, a chord of length $16$ lies $6$ units from the center. What is the area of the circle?
A regular hexagon with side length $6$ is inscribed in a circle. What is the area of the region inside the circle but outside the hexagon?
A sphere has volume $288 π$ . What is its surface area?

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