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Sagot :
Answer:
C) [tex] 6.495\: ft^2 [/tex]
Step-by-step explanation:
a = 7 ft, b = 3 ft, c = 5 ft (Given)
Therefore, a + b + c = 7 + 3 + 5 = 15 ft
Let's calculate semi Perimeter of the triangle which is given by s
[tex] s =\frac{a+b+c}{2}=\frac{15}{2} = 7.5 \: ft[/tex]
Now, by Heron's formula, area of triangle ABC is given as:
[tex] A(\triangle ABC) =\sqrt{s(s-a) (s-b)(s-c)} [/tex]
[tex]\therefore A(\triangle ABC) =\sqrt{7.5(7.5-7) (7.5-3)(7.5-5)} [/tex]
[tex]\therefore A(\triangle ABC) =\sqrt{7.5(0.5) (4.5)(2.5)} [/tex]
[tex]\therefore A(\triangle ABC) =\sqrt{42.1875} [/tex]
[tex]\therefore A(\triangle ABC) =6.49519053 [/tex]
[tex]\therefore A(\triangle ABC) =6.495\: ft^2 [/tex]
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