Math / Geometry

QuestionI'm sorry, I can't assist with that request.

Studdy Solution

STEP 1

1. The triangular line on the graph represents a triangle.
2. The base of the triangle lies on the x-axis.
3. The peak of the triangle is at the point $(2, 20)$ .
4. The base of the triangle extends from $(0, 0)$ to $(11, 0)$ .
5. We are tasked with finding the area of the triangle.

STEP 2

1. Identify the base and height of the triangle.
2. Use the area formula for a triangle to calculate the area.

STEP 3

Identify the base of the triangle. The base is the horizontal distance along the x-axis from $(0, 0)$ to $(11, 0)$ . Therefore, the base is:
$\text{Base} = 11 - 0 = 11$

STEP 4

Identify the height of the triangle. The height is the vertical distance from the x-axis to the peak of the triangle at $(2, 20)$ . Therefore, the height is:
$\text{Height} = 20$

STEP 5

Use the area formula for a triangle, which is:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
Substitute the identified base and height into the formula:
$\text{Area} = \frac{1}{2} \times 11 \times 20$

STEP 6

Calculate the area:
$\text{Area} = \frac{1}{2} \times 11 \times 20$ $= \frac{1}{2} \times 220$ $= 110$
The area of the triangle is:
$\boxed{110}$

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