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First we need to find the side lengths of the squares which is 2 and 3 because Area is is L*W and a square has all of its side the same. So, 2*2=4 and 3*3=9. To find the length and height of rectangle ABCD then we will have to add the length of line segment FG with 2 and 3 as that is the complete length if added together. Therefore the length is 5+3+2=10 cm. The height is just 2+3=5 cm because they stack up to the top if they are on top of each other.Now we know the measurements, we can find the area of the rectangles. We know line FK is 2 cm as it is beside the square with the length of 2 cm and the length is 10 cm - 2 cm = 8 cm as it the total length subtracted by the small length of the square at the end which is again 2. Therefore the first rectangle BHFK is 8*2=16 cm squared. The second square has the width of 3 as it is beside the larger square with 3 as mentioned before. The length is the total length of ABCD subtracted by 3 cm which is the extra amount at the end. So, the length of DEGJ is 10-3= 7 cm. Therefore, the second rectangle DEGJ is 7*3= 21 cm squared. Finally we can add these two areas up to find the total area of the two rectangles which is 16+21= 37 cm squared.
aefk is a 2cm by 2cm (square) and EFGH is 3 by 3(square) and fk is 5 cm the bigger rectangle(DJEG) is 3 by 7 cm which is 21 cm2 and the smaller one(KFBH) is 2 by 8 and is 16cm2
To find EG, I first note that the top-left square is 2 by 2 cm. Therefore, 2 + FG must equal EG, and FG = 5 cm. EG is shown to now be 7 cm.
For ED and GJ (ED = GJ), I note that the bottom right square has dimensions 9 by 9 cm, so ED and GJ are also 9 cm. Now, to find rectangle EDGJ, I find 9 * 7 cm, which is 63 cm squared.
To find FH, I calculate FG + GH, which is 5 + 9 cm (shown by the given measurements). FH = 14 cm.
KF and BH = AE, which is 4 cm (given). Therefore, rectangle KFBH is 14 * 4 cm = 56 cm squared.
The total area of the two rectangles is 56 + 63 cm, which equals 119 cm squared.
I really messed up the calculations of the sides of the removed squares. This is my new answer:
To find EG, I first note that the top left square is 2 by 2 cm (the area is shown to be 4 cm squared). Therefore, 2 + FG must equal EG, and FG = 5 cm. EG is shown to now be 7 cm.
For ED and GJ (ED = GJ), I note that the bottom right square has dimensions 3 by 3 cm (the area is shown to be 9 cm SQUARED), so ED and GJ are also 3 cm. Now, to find rectangle EDGJ, I find 3 * 7 cm, which is 21 cm squared.
To find FH, I calculate FG + GH, which is 5 + 3 cm (shown by the given measurements). FH = 8 cm.
KF and BH (individually) are 2 cm. Therefore, rectangle KFBH is 8 * 2 cm = 16 cm squared.
The total area of the two rectangles is 16 + 21 cm, which equals 37 cm squared.
The area of both shaded rectangles together is 37cm squared. To figure this out, I first had to look at both squares, since AEFK was 4cm squared, I knew that the side lengths were 2cm and same for GJCH which had side lengths of 3cm. Now that I knew that I looked at the rectangles, since the line segment was 5cm, I new I had to add 2cm of AEFK to complete the smaller rectangle and needed to add GJCHs side length to 5cm and multiply the length and width which led me to (8x2)+(7x3)= 3zcm squared
The total area of both the shaded rectangles area added up is 37cm squared. To find this I first tried to find the long sides of the rectangle that were touching line FG. FG is 5cm and all squares have equal side lengths, meaning square AEFK is 2cmx2cm and GHCJ is 3cmx3cm. I simply added the line and the square lengths to get the side lengths of the rectangles. (FG+GH=FH or 5+3=8) (FG+EF=EG or 5+2=7). The other side lengths of the shady rectangles are the same as the 2 square sides, so 7x3=21cm squared for EDGJ and 8x2=16cm squared for KFHB. 16+21=37cm squared.
First, you have to find the square root of 4 so you know the side lengths of square AEKF. The square root is 2. That means that the edge EG on rectangle DEGJ is 7cm (FG+2). Also, that means that edge FK on rectangle BKFH is 2cm. Next, you have to find the square root of 9 to find the side lengths of square GHJC. The square root is 3. That means that edge FH on rectangle BKFH is 8cm (FG+3). That also means that edge GJ on rectangle DEGJ is 3cm, Now I will find the areas of all the rectangles. BKFH=8*2=16cm2 DEGJ=7*3=21cm2 Finally, I'll add the areas together. 16+21=37. The total area of the 2 shaded triangles is 37cm2.
The correct answer was 37 cm squared. It seems many people got this one right. The first 4 students with the correct answer here on the Blog to come see me tomorrow will get a prize.
To find this we had to calculate the area: Rectangle KBHF - (5+3) x 2 cm = 16 cm squared Rectangle EGDJ - (5+2) x 3 cm = 21 cm squared Together - 37 cm squared
KF & BH= square root of 4= 2cm
ReplyDeleteFH & KB= 5cm (FG) + 3cm (square root of 9)=8cm
Therefore area of rectangle KBHF is 2x8=16 cm2
EG & DJ=(Side length of square AEFK) 2cm +5 cm (FG)=7 cm
GJ & ED= 3 (side length of square GHCJ)
Therefore area of rectangle GEDJ is 7x3=21 cm2
21 cm2 + 16 cm2= 37 cm2
The total area of the rectangles are 37 cm2
First we need to find the side lengths of the squares which is 2 and 3 because Area is is L*W and a square has all of its side the same. So, 2*2=4 and 3*3=9. To find the length and height of rectangle ABCD then we will have to add the length of line segment FG with 2 and 3 as that is the complete length if added together. Therefore the length is 5+3+2=10 cm. The height is just 2+3=5 cm because they stack up to the top if they are on top of each other.Now we know the measurements, we can find the area of the rectangles. We know line FK is 2 cm as it is beside the square with the length of 2 cm and the length is 10 cm - 2 cm = 8 cm as it the total length subtracted by the small length of the square at the end which is again 2. Therefore the first rectangle BHFK is 8*2=16 cm squared. The second square has the width of 3 as it is beside the larger square with 3 as mentioned before. The length is the total length of ABCD subtracted by 3 cm which is the extra amount at the end. So, the length of DEGJ is 10-3= 7 cm. Therefore, the second rectangle DEGJ is 7*3= 21 cm squared. Finally we can add these two areas up to find the total area of the two rectangles which is 16+21= 37 cm squared.
ReplyDeleteaefk is a 2cm by 2cm (square) and EFGH is 3 by 3(square) and fk is 5 cm
ReplyDeletethe bigger rectangle(DJEG) is 3 by 7 cm which is 21 cm2 and the smaller one(KFBH) is 2 by 8 and is 16cm2
But it is asking you for the "total". What might that be?
DeleteCheck
ReplyDeleteTo find EG, I first note that the top-left square is 2 by 2 cm. Therefore, 2 + FG must equal EG, and FG = 5 cm. EG is shown to now be 7 cm.
ReplyDeleteFor ED and GJ (ED = GJ), I note that the bottom right square has dimensions 9 by 9 cm, so ED and GJ are also 9 cm. Now, to find rectangle EDGJ, I find 9 * 7 cm, which is 63 cm squared.
To find FH, I calculate FG + GH, which is 5 + 9 cm (shown by the given measurements). FH = 14 cm.
KF and BH = AE, which is 4 cm (given). Therefore, rectangle KFBH is 14 * 4 cm = 56 cm squared.
The total area of the two rectangles is 56 + 63 cm, which equals 119 cm squared.
Correction.
DeleteI really messed up the calculations of the sides of the removed squares. This is my new answer:
To find EG, I first note that the top left square is 2 by 2 cm (the area is shown to be 4 cm squared). Therefore, 2 + FG must equal EG, and FG = 5 cm. EG is shown to now be 7 cm.
For ED and GJ (ED = GJ), I note that the bottom right square has dimensions 3 by 3 cm (the area is shown to be 9 cm SQUARED), so ED and GJ are also 3 cm. Now, to find rectangle EDGJ, I find 3 * 7 cm, which is 21 cm squared.
To find FH, I calculate FG + GH, which is 5 + 3 cm (shown by the given measurements). FH = 8 cm.
KF and BH (individually) are 2 cm. Therefore, rectangle KFBH is 8 * 2 cm = 16 cm squared.
The total area of the two rectangles is 16 + 21 cm, which equals 37 cm squared.
Great correction Sherry. It is in fact 37 cm squared.
DeleteThe area of both shaded rectangles together is 37cm squared. To figure this out, I first had to look at both squares, since AEFK was 4cm squared, I knew that the side lengths were 2cm and same for GJCH which had side lengths of 3cm. Now that I knew that I looked at the rectangles, since the line segment was 5cm, I new I had to add 2cm of AEFK to complete the smaller rectangle and needed to add GJCHs side length to 5cm and multiply the length and width which led me to (8x2)+(7x3)= 3zcm squared
ReplyDeleteI think you made a typo in your response Sivan. Do you see where that might be?
DeleteThe total area of both the shaded rectangles area added up is 37cm squared. To find this I first tried to find the long sides of the rectangle that were touching line FG. FG is 5cm and all squares have equal side lengths, meaning square AEFK is 2cmx2cm and GHCJ is 3cmx3cm. I simply added the line and the square lengths to get the side lengths of the rectangles. (FG+GH=FH or 5+3=8) (FG+EF=EG or 5+2=7). The other side lengths of the shady rectangles are the same as the 2 square sides, so 7x3=21cm squared for EDGJ and 8x2=16cm squared for KFHB. 16+21=37cm squared.
ReplyDeleteFirst, you have to find the square root of 4 so you know the side lengths of square AEKF.
ReplyDeleteThe square root is 2. That means that the edge EG on rectangle DEGJ is 7cm (FG+2).
Also, that means that edge FK on rectangle BKFH is 2cm.
Next, you have to find the square root of 9 to find the side lengths of square GHJC.
The square root is 3. That means that edge FH on rectangle BKFH is 8cm (FG+3).
That also means that edge GJ on rectangle DEGJ is 3cm,
Now I will find the areas of all the rectangles.
BKFH=8*2=16cm2
DEGJ=7*3=21cm2
Finally, I'll add the areas together.
16+21=37.
The total area of the 2 shaded triangles is 37cm2.
Two shaded rectangles Harith. Be careful!
DeleteThe correct answer was 37 cm squared. It seems many people got this one right. The first 4 students with the correct answer here on the Blog to come see me tomorrow will get a prize.
ReplyDeleteTo find this we had to calculate the area:
ReplyDeleteRectangle KBHF - (5+3) x 2 cm = 16 cm squared
Rectangle EGDJ - (5+2) x 3 cm = 21 cm squared
Together - 37 cm squared