Q. If the diagonals of a rhombus are 10 cm and 24 cm, what is the area?
A.
120 cm²
B.
240 cm²
C.
300 cm²
D.
480 cm²
Solution
The area of a rhombus can be calculated using the formula (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals. Here, area = (1/2) × 10 cm × 24 cm = 120 cm².
Q. What is the length of each side of a regular octagon inscribed in a circle of radius 10 cm?
A.
5√2 cm
B.
10 cm
C.
10√2 cm
D.
5 cm
Solution
The length of each side of a regular octagon inscribed in a circle can be calculated using the formula s = r × √2(1 - cos(π/n)). For n=8 and r=10 cm, s = 10 cm × √2(1 - cos(π/8)) = 5√2 cm.
Q. What is the measure of each interior angle of a regular pentagon?
A.
108 degrees
B.
120 degrees
C.
90 degrees
D.
135 degrees
Solution
The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) × 180] / n. For a pentagon (n=5), each angle = [(5-2) × 180] / 5 = 108 degrees.
