Question

analyze the diagram below and complete the statement that follows.
the area of the triangle is ______.
a. 54 u²
b. 120 u²
c. 126 u²
d. 252 u²

Explanation:

Step1: Recall triangle area formula

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \).

Step2: Identify base and height

From the diagram, the base (the side with the right angle) is 21, and the corresponding height (the perpendicular segment to the base) is 12.

Step3: Calculate the area

Substitute base = 21 and height = 12 into the formula: \( A = \frac{1}{2} \times 21 \times 12 \). First, calculate \( 21 \times 12 = 252 \), then \( \frac{1}{2} \times 252 = 126 \).

Answer:

C. 126 \( u^2 \)