Question

Find the area of a triangle whose two sides are 10 inches and 18 inches long, and has a perimeter of 42 inches. a. 30.4 in²

b. 69.65 in²
c. 155.74 in² d. 27.5 in²

Answer 1

To find the area of a triangle, use the formula Area = 1/2 * base * height. Given the lengths of two sides and the perimeter of the triangle, you can solve for the length of the third side using the formula for the perimeter of a triangle. Once you have the lengths of all three sides, you can use Heron's formula to calculate the area.

Step-by-step explanation:

To find the area of a triangle, you can use the formula: Area = 1/2 * base * height. In this case, we are given the lengths of two sides and the perimeter of the triangle. Let's call the two sides that are given as 10 inches and 18 inches, as side A and side B respectively. We can use the formula for perimeter of a triangle to find the length of the third side, side C. The formula for perimeter of a triangle is: Perimeter = side A + side B + side C. Since we know the perimeter is 42 inches and side A and side B are given, we can substitute these values into the equation and solve for side C. Once we have the lengths of all three sides of the triangle, we can use Heron's formula to find the area. Heron's formula for the area of a triangle is: Area = sqrt(s * (s - side A) * (s - side B) * (s - side C)), where s is the semiperimeter of the triangle, calculated as: s = (side A + side B+ side C) / 2. After substituting the lengths of the sides into the formula, we can calculate the area of the triangle.

Answer 2

The area of a triangle with sides measuring 10 inches, 18 inches, and a perimeter of 42 inches is found using Heron's formula. The area is calculated to be approximately 69.65 square inches, which corresponds to option b.

Step-by-step explanation:

To find the area of a triangle with two sides of 10 inches and 18 inches and a perimeter of 42 inches, we first need to determine the length of the third side. The perimeter is the sum of all three sides, so the third side can be found by subtracting the known sides from the total perimeter: 42 inches - (10 inches + 18 inches) = 14 inches for the third side.

Now, we can use Heron's formula to find the semi-perimeter (s), which is half of the perimeter: s = (10 + 18 + 14) / 2 = 21 inches. Next, we apply Heron's formula to find the area (A):
A = √ [s(s - a)(s - b)(s - c)],
where a, b, and c are the lengths of the sides of the triangle.

Plugging in the values: A = √ [21(21 - 10)(21 - 18)(21 - 14)] = √ [21*11*3*7] = √ [4851] ≈ 69.65 in².

So, the area of the given triangle is approximately 69.65 square inches (option b).