Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-A stained glass window is composed of 20 triangular sections, each with sides 4,7 , and 8 in. Find the total area of the window (to the nearest square inch).
A) 280 in. $^ { 2 }$
B) 14 in. $^ { 2 }$
C) 91 in. $^ { 2 }$
D) $3849 \mathrm { in } ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the area of a triangle with sides 4, 7, and 8 inches, we can use Heron's formula. First, calculate the semi-perimeter (s) as $s = \frac{4 + 7 + 8}{2} = 9.5$. Then, the area ($A$) of one triangle is given by $\sqrt{s(s - 4)(s - 7)(s - 8)}$, which simplifies to $\sqrt{9.5 \times 5.5 \times 2.5 \times 1.5} \approx 14 \, \text{in}^2$. Since the window is composed of 20 such triangles, the total area is $20 \times 14 = 280 \, \text{in}^2$.

Find the Area of Triangle ABC with the Given Parts 2^ { 2 }2

Find the Area of Triangle ABC with the Given Parts $^ { 2 }$