Question

q3. area of a triangle formed by two radii
on the unit circle let points a and b correspond to angles 0° and 90°, respectively. together with the origin o, they form triangle oab.
what is the area of triangle oab?
a. \\(\frac{1}{4}\\)
b. \\(\frac{1}{2}\\)
c. \\(\frac{\sqrt{3}}{2}\\)
d. 1
e. \\(\frac{\sqrt{3}}{2}\\)

Explanation:

Step1: Identify triangle type

Points A, B on unit circle (radius \( r = 1 \)), angle \( \angle AOB = 90^\circ \) (from \( 0^\circ \) and \( 90^\circ \)). So \( OA = OB = 1 \), right triangle.

Step2: Apply area formula

Area of right triangle: \( \frac{1}{2} \times \text{base} \times \text{height} \). Here, base \( OA = 1 \), height \( OB = 1 \). So area \( = \frac{1}{2} \times 1 \times 1 = \frac{1}{2} \).

Answer:

B. \( \frac{1}{2} \)