Difference between the area of the triangle and square is 25
Step-by-step explanation:
- Step 1: Find the area of the triangle given its 3 sides using the Heron's formula.
Area of the triangle = [tex]\sqrt{s (s-a)(s-b)(s-c)}[/tex] where s = [tex]\frac{a + b + c}{2}[/tex]
⇒ s = (6 + 8 + 10)/2 = 24/2 = 12
[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] = [tex]\sqrt{12(12-6)(12-8)(12-10)}[/tex]
= [tex]\sqrt{12(6)(4)(2)}[/tex] = [tex]\sqrt{576}[/tex] = 24 sq. units
- Step 2: Find the area of the square with perimeter = 28 units.
Perimeter of the square = 4 × side = 28
⇒ Side of the square = 28/4 = 7 units
⇒ Area of the square = (side)² = 7² = 49 sq. units
- Step 3: Find the difference between the area of the square and triangle.
Difference = 49 - 24 = 25
