Question

1. find the area of the figure: image of coordinate grid with triangle abc, points a, d, c on the base, y - axis, x - axis

options:
a. 36
b. 12
c. 6
d. 7

Explanation:

Step1: Determine base and height

From the grid, the base \( AC \) of the triangle spans 4 units (since from \( x = 1 \) to \( x = 5 \), difference is \( 5 - 1 = 4 \)), and the height \( BD \) (vertical segment from \( B \) to \( AC \)) is 3 units (from \( y = 1 \) to \( y = 4 \), difference is \( 4 - 1 = 3 \)).

Step2: Apply triangle area formula

The formula for the area of a triangle is \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Substituting base \( = 4 \) and height \( = 3 \), we get \( A=\frac{1}{2}\times4\times3 \).

Step3: Calculate the area

\( \frac{1}{2}\times4\times3 = 2\times3 = 6 \).

Answer:

C. 6