Question

A rectangle topped by a semicircle. the rectangle has length of 4 meters and width of 3 meters. the circle has diameter 3 meters. a norman window is rectangular on three sides with a semi-circular top. you decide to install a norman window in your family room with the dimensions indicated in the diagram. what is its perimeter? a. 15.71 feet c. 18.45 feet b. 14.23 feet d. 14 feet

Answer 1

The perimeter of the Norman window, which consists of a rectangle and a semicircle is approximately 18.71 meters.

Let's calculate the perimeter of the Norman window, which consists of a rectangle and a semicircle.

The rectangle has a length of 4 meters and a width of 3 meters.

The semicircle has a diameter of 3 meters, which means its radius is 3/2 meters.

Now, let's calculate the perimeter:

Perimeter of the Rectangle:

`\begin{aligned}& P_{\text {rectangle }}=2(\text { length }+ \text { width }) \\& P_{\text {rectangle }}=2(4+3) \\& P_{\text {rectangle }}=2 * 7 \\& P_{\text {rectangle }}=14 \text { meters }\end{aligned}`

Circumference of the Semicircle:

`\begin{aligned}& C_{\text {semicircle }}=\pi * \text { radius } \\& C_{\text {semicircle }}=\pi * (3)/(2) \\& C_{\text {semicircle }}=(3 \pi)/(2) \text { meters }\end{aligned}`

Perimeter of the Norman Window:

`\begin{aligned}& P_{\text {total }}=P_{\text {rectangle }}+C_{\text {semicircle }} \\& P_{\text {total }}=14+(3 \pi)/(2)\end{aligned}`

Now, let's calculate the approximate numerical value:

`\begin{aligned}& P_{\text {total }} \approx 14+(3 * 3.14)/(2) \\& P_{\text {total }} \approx 14+(9.42)/(2) \\& P_{\text {total }} \approx 14+4.71 \\& P_{\text {total }} \approx 18.71 \text { meters }\end{aligned}`

So, the closest option is (c) 18.45 feet. The correct answer is (c) 18.45 feet.

Question:

A rectangle topped by a semicircle. the rectangle has length of 4 meters and width of 3 meters. the circle has diameter 3 meters. a Norman window is rectangular on three sides with a semi-circular top. you decide to install a Norman window in your family room with the dimensions indicated in the diagram. what is its perimeter?

a. 15.71 feet

b. 14.23 feet

c. 18.45 feet

d. 14 feet