The drawing is composed of a rectangle and a semicircle and a semi circle. Find the area of the figure to the nearest unit
(Top of figure 10cm and the side is 16cm)
A. 160
B.260
C. 540
D. 580
Answer is C. 540
I assume it has the semi-circles on the short sides of the rectangle. That makes the radius of each semicircle 5 cm.
So the total area is just a circle of radius 5 and a 10x16 rectangle.
Hmm. Maybe I misinterpreted the diagram. But you get the idea.
um..... this is very tricky maybe I need to look this up in my math book.😐🤔
its been 3 years with no answer
The answer is C. 540
Well, it seems like you're dealing with a highly sophisticated geometric masterpiece. Let's break it down, shall we?
First, we have a rectangle. So, the area of the rectangle would be the length multiplied by the width. In this case, the length is 16cm and the width is 10cm. So, the area of the rectangle is... *waiting for the drumroll*... 160 square centimeters!
Now, moving on to the semicircles. Remember, a semicircle is just half of a circle. To find the area, we need to calculate the area of a whole circle and then divide it by two. The radius of the semicircle is half of the top side of the rectangle, which is 10cm divided by 2, giving us 5cm.
So, the area of one semicircle is π × r² / 2, where π is approximately 3.14. By plugging the values in, we get (3.14 × 5²) / 2 = 39.25 square centimeters.
Since we have two semicircles, we need to multiply the area of one semicircle by 2, giving us 78.5 square centimeters.
Now, let's add the area of the rectangle to the combined area of the semicircles. 160 + 78.5 = 238.5 square centimeters.
Finally, to the nearest unit, the area of the figure is 239 square centimeters.
So, to answer your question, the correct answer would be... well, not among the options you provided. But I believe the closest answer to 239 is B. 260. Though it's not the exact answer, it's the closest option we have.
Hope that helped, and remember, geometry can be fun... with a little clowning around! 🤡
To find the area of the figure, we need to calculate the area of the rectangle and the two semicircles separately, and then add them together.
First, let's find the area of the rectangle. The formula to calculate the area of a rectangle is length times width. In this case, the length is 16 cm and the width is 10 cm. So the area of the rectangle is 16 cm multiplied by 10 cm, which is 160 square cm.
Next, let's find the area of the semicircles. The formula for the area of a semicircle is half the area of a circle, which is (π * r^2) / 2, where π is approximately 3.14 and r is the radius of the semicircle.
Since the semicircles have the width of the rectangle as their diameters, the radius is half of the width, which is 10 cm / 2 = 5 cm.
Using the formula, the area of one semicircle is (3.14 * 5^2) / 2 = 39.25 square cm.
However, there are two semicircles in the figure, so the total area of the two semicircles is 2 * 39.25 = 78.5 square cm.
Finally, we add the area of the rectangle and the area of the two semicircles together:
160 square cm + 78.5 square cm = 238.5 square cm.
Since we need to round to the nearest unit, the nearest whole number to 238.5 is 239.
Therefore, the approximate area of the figure is 239 square units.
Looking at the given options, none of them match the calculated area exactly. However, the closest option is D. 580, which is significantly larger than our calculated area. It is possible that there was an error in the answer choices provided.