Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-A solar reflector is made using 32 identical triangular-shaped mirrors, each having sides $1.7$ meters, $2.3$ meters, $1.4$ meters. What is the total surface area of the reflector (to the nearest square meter)?
A) $45 m ^ { 2 }$
B) $38 \mathrm {~m} ^ { 2 }$
C) $35 \mathrm {~m} ^ { 2 }$
D) $33 \mathrm {~m} ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the area of a triangle with sides of lengths $a$, $b$, and $c$, we can use Heron's formula, which is $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter of the triangle, $s = \frac{a+b+c}{2}$. For the given triangle, $a = 1.7$ meters, $b = 2.3$ meters, and $c = 1.4$ meters, so the semi-perimeter $s = \frac{1.7+2.3+1.4}{2} = 2.7$ meters. Plugging these values into Heron's formula gives $A = \sqrt{2.7(2.7-1.7)(2.7-2.3)(2.7-1.4)} \approx 1.183$ square meters for one triangular mirror. The total surface area for 32 mirrors is $32 \times 1.183 \approx 37.856$, which rounds to $38$ square meters.

Find the Area of Triangle ABC with the Given Parts 1.71.71.7

Find the Area of Triangle ABC with the Given Parts $1.7$