Solve the problem.
-A stained glass window is composed of 20 triangular sections, each with sides 6, 8, and 7 in. Find the total area of the window (to the nearest square inch).
A) $20 \mathrm { in } ^ { 2 }$
B) 407 in. 2
C) $125 \mathrm { in } .2$
D) 4737 in. 2

Question

Solve the problem.
-A stained glass window is composed of 20 triangular sections, each with sides 6, 8, and 7 in. Find the total area of the window (to the nearest square inch). 
A) $20 \mathrm { in } ^ { 2 }$
B) 407 in. 2
C) $125 \mathrm { in } .2$
D) 4737 in. 2

Quizplus · Accepted Answer

The area of a triangle with sides a, b, and c can be found using Heron's formula: Area = $\sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a+b+c}{2}$ is the semi-perimeter. For a triangle with sides 6, 8, and 7 inches, $s = \frac{6+8+7}{2} = 10.5$. Thus, the area of one triangle is $\sqrt{10.5(10.5-6)(10.5-8)(10.5-7)} \approx 20.33 \, \text{in}^2$. For 20 triangles, the total area is $20 \times 20.33 \approx 406.6 \, \text{in}^2$, which rounds to 407 square inches.

Solve the Problem 20in220 \mathrm { in } ^ { 2 }20in2

Solve the Problem $20 \mathrm { in } ^ { 2 }$