Answer:
40.5 square units
Step-by-step explanation:
x > -3 → dashed line at x = 3
→ shading to the right of the line x = 3
y < 6 → dashed line at y = 6
→ shading under the line y = 6
y > x → dashed line at y = x
→ shading above the line y = x
Therefore, we have:
- horizontal line: x = -3
- vertical line: y = 6
- diagonal line: y = x
The vertices of the triangle formed are where the lines intersect with eachother.
As we have a horizontal and vertical line, the point at which they meet is a right angle vertex → (-3, 6)
To find the other two points:
- y = x meets x = -3 at (-3, -3)
- y = x meets y = 6 at (6, 6)
The height of the triangle is the y-value of (-3, 6) less the y-value of (-3, -3):
⇒ height = 6 - (-3) = 9
The base (width) of the triangle is the x-value of (6, 6) less the x-value of (-3, 6):
⇒ base =6 - (-3) = 9
Area of a triangle = 1/2 × base × height
= 1/2 × 9 × 9
= 40.5 square units
