#1
Which of the following is a basic geometric shape?
Rhombus
ExplanationA rhombus is a basic geometric shape characterized by all sides being of equal length.
#2
What is the sum of the interior angles of a pentagon?
540 degrees
ExplanationThe sum of the interior angles of a pentagon is 540 degrees.
#3
What is the formula for the circumference of a circle?
C = 2πr
ExplanationThe circumference of a circle is calculated by multiplying the radius (r) by 2π.
#4
What is the formula for the area of a triangle?
A = 0.5bh
ExplanationThe area of a triangle is calculated by multiplying its base (b) by its height (h) and dividing the result by 2.
#5
What is the formula for the area of a trapezoid?
A = (a + b)h/2
ExplanationThe area of a trapezoid is calculated by adding the lengths of its parallel sides (a and b), multiplying the sum by the height (h), and dividing the result by 2.
#6
What is the formula for the area of a rectangle?
A = lw
ExplanationThe area of a rectangle is calculated by multiplying its length (l) by its width (w).
#7
In a right-angled triangle, what is the relationship between the lengths of the sides?
a^2 + b^2 = c^2
ExplanationThis is the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
#8
Which term is used to describe two angles that add up to 90 degrees?
Complementary angles
ExplanationComplementary angles are two angles whose measures sum up to 90 degrees.
#9
In geometry, what is the term for a line segment that connects two non-adjacent vertices in a polygon?
Diagonal
ExplanationA diagonal is a line segment that connects two non-adjacent vertices in a polygon.
#10
In a right-angled triangle, if one angle is 45 degrees, what is the measure of the other acute angle?
60 degrees
ExplanationIn a right triangle, if one angle is 45 degrees, the other acute angle is 90 - 45 = 45 degrees.
#11
What is the measure of each interior angle in a regular hexagon?
120 degrees
ExplanationIn a regular hexagon, each interior angle measures 120 degrees.
#12
What is the equation of a circle in the Cartesian coordinate system?
x^2 + y^2 = r^2
ExplanationThis is the equation of a circle with center (0,0) and radius (r) in the Cartesian coordinate system.
#13
What is the volume of a cube with a side length of 's'?
V = s^3
ExplanationThe volume of a cube with side length 's' is calculated by raising the side length to the power of 3.
#14
In trigonometry, what is the reciprocal of the tangent function?
Cotangent
ExplanationThe cotangent function is the reciprocal of the tangent function in trigonometry.
#15
In a parallelogram, what is the sum of adjacent angles?
180 degrees
ExplanationAdjacent angles in a parallelogram add up to 180 degrees.