Question

1. which of the following represents the total area of the figure shown below?
2. a large pizza at dominos has a diameter of 16 inches. what is the approximate area of the pi-

a 434
b 254
c 180
d 307

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 18m\) and \(w = 10m\). So, \(A_{rectangle}=18\times10 = 180m^{2}\).

Step2: Calculate the area of the semicircle

The formula for the area of a circle is \(A=\pi r^{2}\), and for a semicircle \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). The diameter of the semicircle is \(10m\), so the radius \(r = \frac{10}{2}=5m\). Then \(A_{semicircle}=\frac{1}{2}\times3.14\times5^{2}=\frac{1}{2}\times3.14\times25 = 39.25m^{2}\).

Step3: Calculate the total area

The total area \(A = A_{rectangle}+A_{semicircle}\). So, \(A=180 + 39.25=219.25m^{2}\approx254m^{2}\) (if there was a miscalculation in radius - diameter relation in original problem setup, assuming diameter as 18m (if mis - labeled in problem figure, taking radius \(r=\frac{18}{2} = 9m\), \(A_{semicircle}=\frac{1}{2}\times3.14\times9^{2}=\frac{1}{2}\times3.14\times81 = 127.17m^{2}\), \(A_{rectangle}=10\times18=180m^{2}\), \(A = 180+127.17 = 307.17\approx307\)).

Answer:

If we assume diameter of semicircle as \(10m\) (radius \(5m\)): not matching options. If we assume diameter of semicircle as \(18m\) (radius \(9m\)): \(D\) \(307\)