Find the area.

a = [?]ft²
10 ft, 9 ft and 10 ft
JUST FIGURE IT OUT RIGHT!

1 answer

To calculate the area with the dimensions provided (10 ft, 9 ft, and 10 ft), it appears you are describing a triangle (as the dimensions suggest a triangular shape).

We can use Heron’s formula to find the area of a triangle when the lengths of all three sides are known. Here are the steps:

  1. Calculate the semi-perimeter \( s \): \[ s = \frac{a + b + c}{2} = \frac{10 + 9 + 10}{2} = \frac{29}{2} = 14.5 \text{ ft} \]

  2. Apply Heron's formula to find the area \( A \): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] where \( a = 10 \) ft, \( b = 9 \) ft, and \( c = 10 \) ft.

  3. Substitute the values into the formula: \[ A = \sqrt{14.5(14.5 - 10)(14.5 - 9)(14.5 - 10)} \] \[ A = \sqrt{14.5(4.5)(5.5)(4.5)} \]

  4. Calculate each part:

    • \( 14.5 \)
    • \( 4.5 \)
    • \( 5.5 \)
    • \( 4.5 \)

Now, calculate: \[ 14.5 \times 4.5 \times 5.5 \times 4.5 = 14.5 \times 20.25 = 293.0625 \]

  1. Finally, we take the square root: \[ A = \sqrt{293.0625} \approx 17.1 \text{ ft}² \]

Thus, the area of the triangle is approximately \( 17.1 \text{ ft}² \).

So, the final answer is: \[ A \approx 17.1 \text{ ft}² \]