An advertisement board is in the shape of a $$ \Delta $$ with sides that are $$ 16 \mathrm{~m}, 9 \mathrm{~m} $$, and 13 m long. Find the area of the advertisement board. Select one: a. $$ 46 \mathrm{~m}^{2} $$ b. $$ 58.48 \mathrm{~m}^{2} $$ c. $$ 25 \mathrm{~m}^{2} $$ d. $$ 22 \mathrm{~m}^{2} $$

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UpStudy AI · Accepted Answer

Let the sides of the triangle be $$ a = 16 $$, $$ b = 9 $$, and $$ c = 13 $$.

1. Compute the semiperimeter:
   $$
   s = \frac{a + b + c}{2} = \frac{16 + 9 + 13}{2} = \frac{38}{2} = 19
   $$

2. Use Heron's formula to find the area:
   $$
   A = \sqrt{s(s-a)(s-b)(s-c)}
   $$
   Substitute the values:
   $$
   A = \sqrt{19 \times (19-16) \times (19-9) \times (19-13)} = \sqrt{19 \times 3 \times 10 \times 6}
   $$

3. Simplify inside the square root:
   $$
   19 \times 3 \times 10 \times 6 = 3420
   $$
   So,
   $$
   A = \sqrt{3420}
   $$

4. Approximating the square root:
   $$
   \sqrt{3420} \approx 58.48 \, \mathrm{m}^2
   $$

Thus, the area of the advertisement board is approximately $$ 58.48 \, \mathrm{m}^2 $$, which corresponds to option b.
The area of the advertisement board is approximately $$ 58.48 \, \mathrm{m}^{2} $$, so the correct choice is b.

An advertisement board is in the shape of a with sides that are , and 13 m long. Find the area of the advertisement board.
Select one:
a.
b.
c.
d.

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An advertisement board is in the shape of a with sides that are , and 13 m long. Find the area of the advertisement board. Select one: a. b. c. d.