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Please see below for POTW #22 and please check the previous few answers to make sure you've been gettitng the answers, or at least the process, correct!
AS LEON D CLEARLY AND LOUDLY pointed out to the whole world,
I made a mistake in my answer because of a calculating error. Instead of the two parallel sides of the shaded region being 8 and 10 cm, they are 6 and 8 cm. Therefore, the actual perimeter of the shaded region would be 6 + 8 + 2 + 2 = 18 cm (see other calculations above).
To find the perimeter I first found out that the bottom left corner is an equilateral triangle. There are 8 segments and the side length of the whole shape is 16cm so it is 16/8=2cm. We have two side lengths so far for the shaded figure which is two 2cm side lengths. Next, I found out the two other side lengths which are 6 and 8 because from the bottom left triangle again, each segment goes up by 2 cm and the shaded figure has 6cm and 8cm. Finally we can add these four numbers up to find the perimeter of this shape which is 8+6+2+2=18cm I got bored so I solved the area too: First, I found out there is a small equilateral triangle on the bottom left corner of the bigger equilateral triangle. Therefore the 16cm length divided by 8 sections is 3cm. Therefore the shaded region has two side lengths of 2cm. Therefore the shaded figure which is a trapezoid is a regular trapezoid. Next, to figure out the other two side lengths, we will need to figure out the height of the triangle which is DIFFERENT from the length. We can split the triangle in the middle to get two right scalene triangles. To find the height, we can use the Pythagorean Theorem. We already know two side lengths, and we need to find the opposite side length. We know that one side is 8cm (half of 16cm) and 16cm. 8 squared is 64 and 16 squared is 256 so the height of the whole equilateral triangle is 256-64=192 square rooted. Therefore being about 14. Since we know each side length is the same distance from each other and there are 8 segments, we can divide 14 by 8 which is 1.75. Therefore the height of the trapezoid shaded figure is about 1.75. The two bases of the trapezoid are 6 and 8 because starting from the smallest equilateral triangle ascending by twos; the shaded figure has the lines 6 and 8. Now for the trapezoid area formula is A= (B1+B2)/2*H or (6+8)/2*1.75= 12.25cm squared. Furthermore, the area of the shaded figure is approximately 12.25cm squared.
If you look at Leon D and Sherry's answers, you will see that the perimeter of the shaded region is 18cm. Can you see why or how your answer may have differed?
I assume that each segment parallel to AC shorten in order and in equal size from AC, which is 16 cm.
ReplyDeleteTherefore, going downwards in length to B, each segment parallel to AC would be 14, 12, 10, 8, 6, 4, and 2 cm.
I now know that the shaded region has two sides of 8 and 10 cm.
The question states that BA and BC are divided into eight equal segments. Therefore, each segment would be 16 / 8 which is 2 cm.
The sides of the shaded region are 8, 10, 2, and 2 cm. 8 + 10 + 2 + 2 = 22.
The perimeter of the shaded region is 22 cm.
Can you see why you may have a different answer than your peer below? Why do you think that is? Can you explain specifically?
DeleteAS LEON D CLEARLY AND LOUDLY pointed out to the whole world,
DeleteI made a mistake in my answer because of a calculating error. Instead of the two parallel sides of the shaded region being 8 and 10 cm, they are 6 and 8 cm. Therefore, the actual perimeter of the shaded region would be 6 + 8 + 2 + 2 = 18 cm (see other calculations above).
The perimeter of the shaded region is 18 cm.
That's OK Sherry. You seeing the error and correcting it is the most important part!
DeleteGreat job in seeing that through the calculations of each section the perimeter of the shaded region is 18cm.
Each segment line will decrease by 2 cm
ReplyDelete1st: 16cm
2nd: 14cm
3rd: 12cm
4th: 10cm
5th: 8cm
6th: 6cm
7th: 4cm
8th: 2cm
The segment is 8cm+6cm+2cm+2cm=18cm perimeter
Can you see why you may have a different answer than your peer above? Why do you think that is? Can you explain specifically?
Deletebecause sherry calculated the perimeter of the wrong segment
DeleteTo find the perimeter I first found out that the bottom left corner is an equilateral triangle. There are 8 segments and the side length of the whole shape is 16cm so it is 16/8=2cm. We have two side lengths so far for the shaded figure which is two 2cm side lengths. Next, I found out the two other side lengths which are 6 and 8 because from the bottom left triangle again, each segment goes up by 2 cm and the shaded figure has 6cm and 8cm. Finally we can add these four numbers up to find the perimeter of this shape which is 8+6+2+2=18cm
ReplyDeleteI got bored so I solved the area too:
First, I found out there is a small equilateral triangle on the bottom left corner of the bigger equilateral triangle. Therefore the 16cm length divided by 8 sections is 3cm. Therefore the shaded region has two side lengths of 2cm. Therefore the shaded figure which is a trapezoid is a regular trapezoid. Next, to figure out the other two side lengths, we will need to figure out the height of the triangle which is DIFFERENT from the length. We can split the triangle in the middle to get two right scalene triangles. To find the height, we can use the Pythagorean Theorem. We already know two side lengths, and we need to find the opposite side length. We know that one side is 8cm (half of 16cm) and 16cm. 8 squared is 64 and 16 squared is 256 so the height of the whole equilateral triangle is 256-64=192 square rooted. Therefore being about 14. Since we know each side length is the same distance from each other and there are 8 segments, we can divide 14 by 8 which is 1.75. Therefore the height of the trapezoid shaded figure is about 1.75. The two bases of the trapezoid are 6 and 8 because starting from the smallest equilateral triangle ascending by twos; the shaded figure has the lines 6 and 8. Now for the trapezoid area formula is A= (B1+B2)/2*H or (6+8)/2*1.75= 12.25cm squared. Furthermore, the area of the shaded figure is approximately 12.25cm squared.
If you look at Leon D and Sherry's answers, you will see that the perimeter of the shaded region is 18cm. Can you see why or how your answer may have differed?
ReplyDelete