Enter the known parameters such as: Base and height, Three sides, Two sides and the included angle or One side and two adjacent angles, find the area of a triangle easily.
If the base is \( b \) and the height is \( h \), the area \( A \) is: \( A = \frac{1}{2} \times b \times h \)
Given the three sides \( a \), \( b \), and \( c \), first calculate the semi-perimeter \( s \): \( s = \frac{a + b + c}{2} \) The area \( A \) is: \( A = \sqrt{s \times (s - a) \times (s - b) \times (s - c)} \)
Given two sides \( a \) and \( b \), and the included angle \( C \), the area \( A \) is: \( A = \frac{1}{2} \times a \times b \times \sin(C) \)
If the known side is \( a \), and its opposite angle is \( A \), with adjacent angles \( B \) and \( C \), calculate the third angle as: \( A = 180^\circ - B - C \quad \text{(or } \pi - B - C \text{ for radians)} \) Using the law of sines, the area \( A \) is: \( A = \frac{a^2 \times \sin(B) \times \sin(C)}{2 \times \sin(A)} \)
Solution:
\( A = \frac{1}{2} \times 10 \times 5 = 25 \)
Result: The area is 25.
Solution:
Calculate the semi-perimeter \(s\):
\( s = \frac{7 + 8 + 9}{2} = 12 \)
Calculate the area \(A\):
\( A = \sqrt{12 \times (12 - 7) \times (12 - 8) \times (12 - 9)} = \sqrt{12 \times 5 \times 4 \times 3} = \sqrt{720} \approx 26.83 \)
Result: The area is approximately 26.83.
Solution:
\( A = \frac{1}{2} \times 6 \times 8 \times \sin(45^\circ) \approx \frac{1}{2} \times 6 \times 8 \times 0.7071 = 16.97 \)
Result: The area is approximately 16.97.
Solution:
Calculate the third angle \(A\):
\( A = 180^\circ - 45^\circ - 60^\circ = 75^\circ \)
Calculate the area:
\( A = \frac{10^2 \times \sin(45^\circ) \times \sin(60^\circ)}{2 \times \sin(75^\circ)} \approx \frac{100 \times 0.7071 \times 0.8660}{2 \times 0.9659} \approx 31.69 \)
Result: The area is approximately 31.69.