Question

8. A triangle has sides with lengths of 6, 8, and 10 units, and a square has a

Answer 1

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 = $\sqrt{s (s-a)(s-b)(s-c)}$ where s = $\frac{a + b + c}{2}$

⇒ s = (6 + 8 + 10)/2 = 24/2 = 12

$\sqrt{s(s-a)(s-b)(s-c)}$ = $\sqrt{12(12-6)(12-8)(12-10)}$

                                    = $\sqrt{12(6)(4)(2)}$ = $\sqrt{576}$ = 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