Find the area of the triangle.
it shows 7cm, 11cm, 13cm, and on the inside it shows 5cm
To find the area of the triangle, we can use Heron's formula.
Heron's formula states that the area of a triangle with sides of lengths a, b, and c is given by:
Area = sqrt[s(s-a)(s-b)(s-c)]
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c) / 2
In this case, the sides of the triangle are 7 cm, 11 cm, and 13 cm, and the semi-perimeter is:
s = (7 + 11 + 13) / 2 = 15.5 cm
Now we can plug these values into the formula to find the area:
Area = sqrt[15.5(15.5 - 7)(15.5 - 11)(15.5 - 13)]
Area = sqrt[15.5 * 8.5 * 4.5 * 2.5]
Area = sqrt[1463.375]
Area ≈ 38.25 cm²
Therefore, the area of the triangle is approximately 38.25 cm².
it can either be 32.5cm over 2
45.5cm over 2
65cm over 2
71.5cm over 2
To find the area of a triangle given the lengths of its sides, we can use Heron's formula.
Heron's formula states that the area of a triangle with sides of lengths a, b, and c is given by:
Area = √[s(s - a)(s - b)(s - c)]
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c) / 2
In this case, the sides of the triangle are 7cm, 11cm, and 13cm, with the inside length of 5cm. The semi-perimeter is calculated as:
s = (7 + 11 + 13) / 2
s = 31 / 2
s = 15.5
Now, substitute the values into Heron's formula to find the area:
Area = √[15.5(15.5 - 7)(15.5 - 11)(15.5 - 13)]
Area = √[15.5(8.5)(4.5)(2.5)]
Area = √[1463.375]
Area ≈ 38.25 cm²
Therefore, the area of the triangle is approximately 38.25 cm².
wrong, pick one those
I apologize for the error. Let's reexamine the options provided:
Area = 32.5 cm²
32.5 = sqrt[15.5(15.5 - 7)(15.5 - 11)(15.5 - 13)]
32.5 = sqrt[15.5(8.5)(4.5)(2.5)]
32.5 = sqrt[1463.375]
This calculation is incorrect, so the area is not 32.5 cm².
Area = 45.5 cm²
45.5 = sqrt[15.5(15.5 - 7)(15.5 - 11)(15.5 - 13)]
45.5 = sqrt[15.5(8.5)(4.5)(2.5)]
45.5 = sqrt[1463.375]
This calculation is also incorrect, so the area is not 45.5 cm².
Area = 65 cm²
65 = sqrt[15.5(15.5 - 7)(15.5 - 11)(15.5 - 13)]
65 = sqrt[15.5(8.5)(4.5)(2.5)]
65 = sqrt[1463.375]
This calculation is also incorrect, so the area is not 65 cm².
Area = 71.5 cm²
71.5 = sqrt[15.5(15.5 - 7)(15.5 - 11)(15.5 - 13)]
71.5 = sqrt[15.5(8.5)(4.5)(2.5)]
71.5 = sqrt[1463.375]
Since the calculated area of approximately 38.25 cm² did not match any of the provided options, the correct area calculation based on the given side lengths must lie between those values and does not exactly match any option.