A rectangular piece of paper with length 35 cm and width 14 cm has two semicircles cut out of it, as shown below.

Mathematics

1 answer:

Ede4ka [16]3 years ago

3 0

Answer: 336.14 cm²

Step-by-step explanation:

To find the area of the rectangle after being cut, we want to find the area of the two semicircles and subtract it from the area of the rectangle. The area of the rectangle is just base times height, or 35cm times 14cm = 490cm² . Since there are two semicircles with the same diameter, we can just solve for the area of a circle and subtract it. To find the area of the circle, we need the radius, which we get by dividing the diameter by 2. After that, we calculate the radius to be 7cm, squared and multiplied by 3.14 (area of a circle) to get 153.86 cm². Subtract the areas, and we get 490 - 153.86 = 336.14 cm²

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Can anyone give a step-by-step guide on how to answer these types of questions? I'm really struggling with similar shapes so tha

Dafna11 [192]

Answer:

a) 8cm

b) 19.8cm

Step-by-step explanation:

The key to these types of questions is to keep proportions in mind.

To solve the first question, you want to find the proportion of the smaller triangle to the bigger triangle. The length of AE is 6cm, but the length of AD is (6+4) = 10cm. So the proportion of the bigger triangle to the smaller triangle is 10/6. So to find the lengths of the sides of the bigger triangle, we want to keep this number in mind.

The BE side is parallel to CD, so we have to use length of BE multiplied by the proportion in order to get the length of CD.

CD = 4.8 * (10/6) = 8

CD = 8cm

For the second question, you use the same concept to find all the other side lengths. The only one you need left for the shape EBCD is side BC. Do the same thing you did before, take the length of the side of the smaller triangle that corresponds with side AC on the bigger triangle. In this case, it's AB, which is 4.5cm. Multiply this by 10/6 to get AC.

AC = 4.5 * (10/6) = 7.5

AC = 7.5

But we're not done. We just found the length of AC, but we need the length of BC to calculate the perimeter. To do this, we want to take the length of AC - the length of AB.

7.5 - 4.5 = 3

So the length of BC is 3cm. Now, to find the perimeter, just add all the sides of EBCD together.

4.8 + 4 + 8 + 3 = 19.8cm.

Hope this helps.

8 0

2 years ago

Read 2 more answers

A taxi driver had 50 fares to and from the airport last Monday. The price for a ride to the airport is $10, and the price for a

Rina8888 [55]

Answer:

Number of Fares to airport is 25 and number of fares from airport is 25.

Step-by-step explanation:

Given:

Total Number of fares =50

Let number of fares to airport be x.

Let number of fares from airport be y.

hence the equation can be framed as;

$x+y=50 \ \ \ \ equation \ 1$

Also Given

Total Money Collected = $375

Cost to airport = $10

Cost from Airport = $5

Total Money Collect is equal to Cost to airport multiplied by number of Fares to airport plus Cost from airport multiplied by number of Fare from airport.

$10x+5y=375$