Answer: 57.65 centimeters
Step-by-step explanation:
To find the area of a triangle with side lengths of 5 cm, 19 cm, and 27 cm, you can use Heron's formula. Heron's formula states that the area (A) of a triangle with side lengths a, b, and c can be calculated using the formula:
�
=
�
(
�
−
�
)
(
�
−
�
)
(
�
−
�
)
A=
s(s−a)(s−b)(s−c)
Where
�
s is the semi-perimeter of the triangle, calculated as:
�
=
�
+
�
+
�
2
s=
2
a+b+c
Given the side lengths a = 5 cm, b = 19 cm, and c = 27 cm, we can calculate the semi-perimeter:
�
=
5
+
19
+
27
2
=
51
2
=
25.5
s=
2
5+19+27
=
2
51
=25.5
Now, we can use Heron's formula to find the area:
�
=
25.5
(
25.5
−
5
)
(
25.5
−
19
)
(
25.5
−
27
)
A=
25.5(25.5−5)(25.5−19)(25.5−27)
�
=
25.5
×
20.5
×
6.5
×
(
−
1.5
)
A=
25.5×20.5×6.5×(−1.5)
�
=
25.5
×
20.5
×
6.5
×
1.5
A=
25.5×20.5×6.5×1.5
�
=
3329.0625
A=
3329.0625
�
≈
57.65
cm
2
A≈57.65cm
2
So, the area of the triangle is approximately 57.65 square centimeters.
