Area of a right triangle = ab/2
where a and b are both legs of the triangle.
A) a = 8 inches ; b = 12 inches
A = (8in x 12in)/2 = 96/2 = 48 in²
B.) a = 8 inches ; b = ? ; hypotenuse = 12 inches
Pythagorean theorem is used to get the measurement of the hypotenuse. It can also be used to get the measurement of the missing leg.
a² + b² = c² ⇒ b² = c² - a²
b² = 12² - 8²
b² = 144 - 64
b² = 80
b = √80
b = 8.94
A = ab/2 ⇒ (8 inches * 8.94 inches)/2
A = 71.52 in² / 2
A = 35.76 in²