CALCULATION FORMATION - Marishka S.
Calculate the missing length. Explain your method.
Q1There is a triangle with a perimeter of 6.7cm, with sides that are 1.8cm and 2.4cm, so the question is what is the missing length of 3rd side. To answer this question I . . .
Subtract the 2 side’s length from the overall perimeter because a triangle is made of 3 sides and to find the length of the 3rd you would simply need to subtract the two sides from the perimeter so . . .
6.7 (perimeter) – 1.8 (L of side 1) - 2.4 (L of side 2) = 2.5 (L of missing side)
In conclusion the missing length of side 3 is 2.5cm.
Q2 There is a polygon with a perimeter of 28.5 cm, along with sides that are 3.9cm, 6.6cm and 7.8cm, so what is the missing length of the 4th side?
In order to find the answer to this question, you would need to follow the same routine as Q1. To answer this question you subtract all the sides’ length from the perimeter, since there are 4 sides with 3 that already have their perimeter labeled you would need to find the length of the 3rd side by. . .
28.5cm (perimeter) – 7.8cm (L of side 1) – 3.9cm (L of side 2) – 6.6cm (L of side 3) =10.2cm (L of missing side) I conclusion the length of the 4th missing side is 10.2cm.
Calculate the area of each figure. Describe your method.
Q3 This particular polygon is a regular polygon, so its sides and angles are congruent. Though this shape is not a shape that one sees very often, and it is not a rectangle so you cannot times length by width, instead there are other ways to do this. BUT before I explain how to find the area, everyone needs to know the length of the missing side.
19cm is the length of the whole base but the top is much shorter and thankfully both have the measurement listed so . . . all one would need to do is subtract 19 (bottom base) by 11.2 (top) to get 7.8cm because you would need the length of that to find the area of the 2nd rectangle. Now, did you know that this polygon has two rectangles within it so it would be quite to simple to just calculate the length times the width of each and then add them together, and so that’s what I did to get the full area of the complete polygon.
Calculations: Rectangle 1: 11.2cm (L) x 12cm (W) = 134.4cm2
Rectangle 2: 7.4cm (L) x 2cm (W) = 15.6cm2
Now add . . . 134.4cm2 + 15.6cm2 = 150cm2
In conclusion the area of the polygon in Q3 is 150cm2.
Q4 This also is a regular polygon that can be divided into 2 separate rectangles similar to the previous one. BUT like before I first need to find the length of the one side that does not have its length listed. So I subtract the top width from the bottom base because the base has a longer length, 9.5cm – 4.9cm = 4.6cm. Now can’t forget that the whole purpose of this was to find the area so I once again x L by the W to find the area of each rectangle.
Calculations; Rectangle 1: 4.6cm (L) x 5.7cm (W) = 26.22cm2
Rectangle 2: 4.9cm (L) x 11.4cm (W) = 55.86cm2
Now add . . . 26.22cm2 + 55.86cm2 = 82.08cm2
In conclusion the area of the polygon in Q4 is 82.08cm2
Calculate for each polygon.
Q5 A. The area of the auditorium.
Perhaps you have noticed that all parallelograms look a lot like slanted rectangles or squares. When I’m calculating the area of a parallelogram I always imagine that I have unslanted this figure so it looks like any ordinary square or rectangle. I tend to use this method a lot, I mostly calculate it the same way as well, but things change in parallelograms, instead of doing length x width like a rectangle you would need to do base x height instead. So . . . I would calculate the area by multiplying them, 45m (B) x 40m (H) = 1800m2 (A)
So the simple conclusion would be that the area of the auditorium in Q5a is 1800m2.
B. The area and perimeter of the wall tile.
Another parallelogram! Let’s start with area. First in my mind I form an image of the same figure except this is unslanted. Now I multiply the base by the height of the polygon so it would be 5cm (H) x 12cm (B) = 60cm2 (A). So that is the area of this polygon, 60cm2, but what is its perimeter? In my mind I continue to keep the image unslanted and then I remember that this is a rectangle and all rectangle have 2 pairs of parallel sides so I all I need to do is calculate by adding up the sides. I know that the L is 12cm and the W is 5cm so I add 5cm + 12cm x2 because I can’t forget that they are parallel sides so they each have a pair with the same length and the answer is . . . 34cm. The perimeter of the wall tile is 34cm and the area of the wall tile is 60cm2.
C. The area and perimeter of the table top.
Parallelogram again! JI’ll describe this one in steps. First slant image in mind (not necessary but helps). Now times 1.5m x 1.5m = 2.25m2, this is area. Next for perimeter x 1.5cm by 4 because this figure is a square and square have 4 sides all with the same length like this one, the answer to this is 6cm. So the area of the table top is 2.25cm2 and the perimeter of the table top is 6cm.
Calculate the perimeter and area of each figure.
Q6 This shape when you first look at it looks like it is a shape that you will have some difficulty finding the area of but like I said before ALL shapes can be split to make smaller shapes that you can easily find the area of, but enough talk let’s get started. First split this image into smaller rectangles, I made 3 . . . as shown. Then I found the area of each one separately.
Calculations; Rectangle 1; 1.2cm (W) x 2.7cm (H) = 3.24cm2
Rectangle 2; 1.2cm (W) x 2.7cm (H) = 3.24cm2
Rectangle 3; 6.5cm (W) x 12.8cm (H) = 83.2cm2
Now add . . . 3.24cm2 + 3.24cm2 + 83.2cm2 = 89.68cm2
The area of this figure is 89.68cm2.
Now Perimeter, this gets a little tricky because on of the sides is not labeled so it isn’t all just adding. But don’t fret; finding the measurement of a side is easy. As you can see, the length of this figure is 12.8cm and at the top there are two other congruent measurements that determine the value of the missing factor so now what you do is add 2.7cm to 2.7cm and then subtract the value from 12.8cm and the answer, which is 7.4cm will be revealed. Now this missing value will help find the perimeter. All one has to do now is add the measurement of all the sides together to create the sum also know as the perimeter of this figure.
2.7cm + 1.2cm + 7.4cm + 1.2cm + 2.7cm + 6.5cm + 12.8cm + 6.5cm = 41cm
So the perimeter of this figure is 41cm.
Q7 WOW! This is going to take some work. When I first saw this figure I automatically saw a parallelogram although it isn’t, the sides appear to be slanted. Also there are 2 sets of parallel sides, BUT enough observations. I will describe this in a step by step method to finding area and perimeter to create less confusion, I’ll start with area.
- I slant image in my mind (not necessary but helps)
- I create two rectangles to make it easier to calculate area.
- Calculate area of Rectangle 1 14.3cm (B) x 12.2cm (H) = 174.46cm2
- Find length of missing value 14.3cm - 7.6cm =6.7cm
- Calculate area of rectangle 2 6.7cm (B) x 1.3cm (H) = 8.71cm2
- Add up areas of rectangles 174.46cm2 (R1) + 8.71cm2 (R2) = 183.17cm2
There we go, that gives me an answer of 183.17cm2 which is the area of this figure.
Now all that is left is the perimeter. Since I already found the missing value all I need to do is add up the measurement for all the sides, here we go . . .
14.3cm + 16cm + 6.7cm + 3.8cm + 7.6cm + 12.2cm = 60.6cm
That’s it. 60.6cm is the perimeter of this figure.
Wordier Problems . . .
Q8 A Builder charges $660.00 for a fence around 3 sides of a square deck. Each side of the deck is 5.5m. What is the cost per meter of fence?
There is a square deck that needs to be fenced but what is the cost per fence? Well, first off 3 sides are being fenced and we know that, each side is 5.5m so we need to multiply that by 3; 5.5m x 3 = 16.5m. Now we need to figure the cost of it. There is exactly 16.5m of fencing and the cost of this is $660.00, so we simply divide $660.00 ÷ 16.5m = $40. So the cost of a meter of fencing is $40.
Q9 A kitchen counter measures 210cm by 60cm. The hole cut out for the sink is 78cm by 46cm. What is the area of working surface on the counter?
In this particular question you also need to do subtraction, but first we start with multiplication. One would need to multiply to find the areas of both the counter and the sink. 210cm x 60cm = 12600cm2 and for the sink 78cm x 46cm = 3588cm2. Now one needs to subtract the sink’s area from the counter’s area because most people don’t work and cook in the sink and we only want the area of the working surface on the counter. 12600cm2 – 3588cm2 = 9012cm2. 9012cm2 is working surface on the kitchen counter.
Q10 A. The Chaus put a garden at one end of their rectangular yard and a patio at the other. They put sod in the middle.
Calculate the area of the sod.
Because the shape of the sod is in the form of a parallelogram, I would have to do the parallelogram formula to get the area, so I would do b x h = Area. So, 15.2m x 8.5m = 129m2. The area of the sod is 129m2.
B. Sod costs $15.75/m2. Calculate the total cost of the sod.
It’s a good thing that we already have the sod area in m2, now I need to multiply the area of sod by its cost. 129m2 x $15.75 = $2031.75. The cost of 129m2 of sod is $2031.75.
C. The patio and the garden are of the same size. What is the area of each?
The patio and garden are both in the form of a triangle, so I need to use the triangle area method to find their area, which is base x altitude ÷ 2 = area.
No comments:
Post a Comment