Question

What is the area of a triangle (picture provided)

Answer 1

Area Δ = 6.4 units² ⇒ the answer is (c)

Explanation:

* Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 2 , b = 7 , c = 8

∴ cos(C) = (2² + 7² - 8²)/2(2)(7) = 4 + 49 - 64/28 = -11/28

∴ m∠C = 113.1°

∴ Area Δ = (1/2)(2)(7)sin(113.1) = 6.4 units²

Answer 2

C

Explanation:

Use the Heron's formula for the area of the triangle:

`A=√(p(p-a)(p-b)(p-c)),`

where a, b, c are lengths of triangle's sides and
`p=(a+b+c)/(2).`

Since
`a=2,\ b=7,\ c=8,` then

`p=(2+7+8)/(2)=8.5.`

Hence,

`A=√(8.5(8.5-2)(8.5-7)(8.5-8))=√(8.5\cdot 6.5\cdot 1.5\cdot 0.5)=\\ \\=√(41.4375)\approx 6.4\ un^2.`