Question

The accompanying diagram shows a triangular plot of land located in Moira’s garden. Find the area of the plot of land, and round your answer to the nearest hundred square feet.
BCA
B= 160 ft
C=135 ft
A=125 ft



Question 4 options:

8400


8200


8100


8500

Answer 1

To find the area of a triangle given the lengths of its sides, we can use Heron's formula. First, we need to calculate the semi-perimeter (s) of the triangle.

The formula for the semi-perimeter is:

\[ s = \frac{A + B + C}{2} \]

In this case:

- \( A = 125 \, \text{ft} \)
- \( B = 160 \, \text{ft} \)
- \( C = 135 \, \text{ft} \)

Calculating the semi-perimeter:

\[ s = \frac{125 + 160 + 135}{2} = \frac{420}{2} = 210 \, \text{ft} \]

Now we can use Heron's formula to find the area (A):

\[ A = \sqrt{s(s - A)(s - B)(s - C)} \]

Substituting in the values we have:

\[ A = \sqrt{210 \times (210 - 125) \times (210 - 160) \times (210 - 135)} \]

Calculating each term inside the square root:

- \( s - A = 210 - 125 = 85 \)
- \( s - B = 210 - 160 = 50 \)
- \( s - C = 210 - 135 = 75 \)

Now, plugging these values back in:

\[ A = \sqrt{210 \times 85 \times 50 \times 75} \]

Calculating the product:

First, calculate \( 85 \times 50 \):

\[ 85 \times 50 = 4250 \]

Now calculate \( 4250 \times 75 \):

\[ 4250 \times 75 = 318750 \]

Now we have:

\[ A = \sqrt{210 \times 318750} \]

Calculating the product:

\[ 210 \times 318750 = 66862500 \]

Now take the square root:

\[ A = \sqrt{66862500} \approx 8183.74 \, \text{sq ft} \]

Rounding to the nearest hundred square feet gives us:

**8100 square feet**

Thus, the correct answer from the options is:

**8100**