Question content area top left
Part 1
A triangular lot is 140 ft on one side and has a property line of length 900 ft. Find the area of the lot in acres.​ (Figure not drawn to​ scale)
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Question content area top right
Part 1
140
900
Property line
Question content area bottom
Part 1
Areaalmost equals
  
enter your response here ​acre(s)
​(Round to the nearest hundredth as​ needed.)

To solve this problem, we need to find the area of a triangular lot using the given side lengths and then convert that area to acres.

The formula to find the area of a triangle when two sides and the angle between them are known is:

\[
\text{Area} = \frac{1}{2} \times a \times b \times \sin(\theta)
\]

However, from the information given, we don't have the angle \(\theta\) between the two sides of the triangle (140 ft and 900 ft). Assuming the question refers to a right triangle, where the angle between the sides is 90°, we can simplify the formula for the area:

\[
\text{Area} = \frac{1}{2} \times 140 \, \text{ft} \times 900 \, \text{ft}
\]

Now, let's calculate that.

\[
\text{Area} = \frac{1}{2} \times 140 \times 900 = 63,000 \, \text{square feet}
\]

Next, we need to convert this area into acres. There are 43,560 square feet in an acre, so:

\[
\text{Area in acres} = \frac{63,000}{43,560} \approx 1.45 \, \text{acres}
\]

So, the area of the triangular lot is approximately **1.45 acres**.

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Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:

1. How would the area change if the angle between the sides wasn't 90°?
2. What is the formula for the area of a triangle using only the side lengths and an included angle?
3. How do you convert square feet to square meters?
4. If the triangle had different side lengths, how would that affect the area?
5. How does the concept of right triangles relate to the Pythagorean theorem?

**Tip:** In problems where angles are missing, assume a right triangle if no further details are provided, unless specified otherwise.

A triangular lot is 140 ft on one side and has a property line of length 900 ft. Find the area of the lot in acres. (Figure not drawn to scale) (Round to the nearest hundredth as needed.)

Learn how to find the area of a triangular lot with one side of 140 ft and a property line of 900 ft. This solution uses geometric principles and unit conversions to calculate the area in acres. Suitable for high school students.

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