its A: The area of ΔABC > the area of ΔXYZ
Step-by-step explanation:
Using the Heron's formula and sine formula to find the areas of ΔABC and ΔXYZ respectively, the statement that is true about their relative areas is: A. The area of ΔABC > the area of ΔXYZ.
The Heron's formula is applied to find the area of a triangle if we are given only three sides of a triangle, a, b, and c.
Heron's formula = [tex]\sqrt{s(s - a)(s - b)(s - c)}[/tex], where:
s = semi-perimeter = (a + b + c)/2
Use the Heron's Formula to find the area of ΔABC:
a = 6
b = 7
c = 4
s = (6 + 7 + 4)/2 = 8.5
Area of ΔABC = [tex]\sqrt{8.5(8.5 - 6)(8.5 - 7)(8.5 - 4)} = 11.98 $ sq. units\\\\[/tex]
Use sine formula to find the area of ΔXYZ
Area of ΔXYZ = 1/2(2 × 12)sin 98° = 11.88 sq. units.
Therefore, using the Heron's formula and sine formula to find the areas of ΔABC and ΔXYZ respectively, the statement that is true about their relative areas is: A. The area of ΔABC > the area of ΔXYZ.
Learn more about the Heron's formula on:
https://brainly.com/question/10677686
