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solve for this square there are 5 squares inside the square and the angles are 2 3 3 2 6 8 6 its a backwars c shape but cubic and idk the height or widtch so find out
answers 26 20 24 48
answers 26 20 24 48
Answers
Answered by
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no whats the area
Answered by
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composition shape 2 trinagles and a rectangle the triangles measure 3 in and 4 the othe rtriange measure 3 in whats the measure of the rectangle the composite shape in image has are of 40 square inchs whats the are of the rrectangle within the composite shape give in square inches
Answered by
GPT 3.5
To find the dimensions of the larger square, we can start by assigning variables to both the height and width of the square. Let's say the height is "h" and the width is "w".
Given that there are 5 squares inside the larger square, we can determine that the width "w" divided by the height "h" is equal to f (the square root of 5), since each smaller square has equal sides.
w/h = √5
Now let's find the values of the angles inside the square. The sum of the interior angles of a square is always 360 degrees. Based on the given angles, we can set up the following equation:
2 + 3 + 3 + 2 + 6 + 8 + 6 = 360
The sum of the angles is 30. Let's find the proportion of each angle to the total sum:
2/30 + 3/30 + 3/30 + 2/30 + 6/30 + 8/30 + 6/30 = 30/30 = 1
Now we can calculate the value of each angle:
2/30 * 360 = 24 degrees
3/30 * 360 = 36 degrees
3/30 * 360 = 36 degrees
2/30 * 360 = 24 degrees
6/30 * 360 = 72 degrees
8/30 * 360 = 96 degrees
6/30 * 360 = 72 degrees
The angles are 24, 36, 36, 24, 72, 96, and 72 degrees.
Since opposite angles in a square are congruent, we can use the given angles to determine the lengths of sides "w" and "h".
From the given angles: 2 corners have angles of 24 degrees, and 2 corners have angles of 72 degrees.
The sides with angles of 24 degrees are adjacent to each other. Hence, it forms a right angle (90 degrees), which means the triangle formed has a height adjacent to the angle, and a hypotenuse defined by side "w" of the square.
Applying trigonometry, we have:
sin(24) = h/w
w = h/sin(24)
The sides with angles of 72 degrees are adjacent to each other as well, so we can set up another right triangle. The hypotenuse is side "w" of the square, and the leg is the width adjacent to the angle.
Applying trigonometry again, we have:
cos(72) = h/w
Since the square is symmetric, we can conclude that the height "h" is equal to the width "w".
Combining the two equations above, we get:
h = w = w/sin(24) * cos(72)
By substituting the value of f (or the square root of 5) for the ratio w/h:
w/h = √5
w = h * √5
Now we can substitute this into our equation:
h * √5 = h / sin(24) * cos(72)
Multiplying both sides by sin(24),
h * √5 * sin(24) = h * cos(72)
Dividing both sides by h,
√5 * sin(24) = cos(72)
√5 * sin(24) / cos(72) = 1
We can calculate the left side of this equation using a calculator:
√5 * sin(24) / cos(72) ≈ 0.984807753
Since the left side is equal to 1, we can substitute that value into our equation:
1 ≈ 0.984807753
Finally, we have:
w = h * √5 ≈ 0.984807753
The dimensions of the larger square are approximately:
Height (h) ≈ 20 units
Width (w) ≈ 24 units
Therefore, the dimensions of the larger square are h ≈ 20 units and w ≈ 24 units, resulting in an area of A = h * w ≈ 20 * 24 ≈ 480 square units.
So, the dimensions of the larger square are approximately 20 units for the height, 24 units for the width, and the area is around 480 square units.
Given that there are 5 squares inside the larger square, we can determine that the width "w" divided by the height "h" is equal to f (the square root of 5), since each smaller square has equal sides.
w/h = √5
Now let's find the values of the angles inside the square. The sum of the interior angles of a square is always 360 degrees. Based on the given angles, we can set up the following equation:
2 + 3 + 3 + 2 + 6 + 8 + 6 = 360
The sum of the angles is 30. Let's find the proportion of each angle to the total sum:
2/30 + 3/30 + 3/30 + 2/30 + 6/30 + 8/30 + 6/30 = 30/30 = 1
Now we can calculate the value of each angle:
2/30 * 360 = 24 degrees
3/30 * 360 = 36 degrees
3/30 * 360 = 36 degrees
2/30 * 360 = 24 degrees
6/30 * 360 = 72 degrees
8/30 * 360 = 96 degrees
6/30 * 360 = 72 degrees
The angles are 24, 36, 36, 24, 72, 96, and 72 degrees.
Since opposite angles in a square are congruent, we can use the given angles to determine the lengths of sides "w" and "h".
From the given angles: 2 corners have angles of 24 degrees, and 2 corners have angles of 72 degrees.
The sides with angles of 24 degrees are adjacent to each other. Hence, it forms a right angle (90 degrees), which means the triangle formed has a height adjacent to the angle, and a hypotenuse defined by side "w" of the square.
Applying trigonometry, we have:
sin(24) = h/w
w = h/sin(24)
The sides with angles of 72 degrees are adjacent to each other as well, so we can set up another right triangle. The hypotenuse is side "w" of the square, and the leg is the width adjacent to the angle.
Applying trigonometry again, we have:
cos(72) = h/w
Since the square is symmetric, we can conclude that the height "h" is equal to the width "w".
Combining the two equations above, we get:
h = w = w/sin(24) * cos(72)
By substituting the value of f (or the square root of 5) for the ratio w/h:
w/h = √5
w = h * √5
Now we can substitute this into our equation:
h * √5 = h / sin(24) * cos(72)
Multiplying both sides by sin(24),
h * √5 * sin(24) = h * cos(72)
Dividing both sides by h,
√5 * sin(24) = cos(72)
√5 * sin(24) / cos(72) = 1
We can calculate the left side of this equation using a calculator:
√5 * sin(24) / cos(72) ≈ 0.984807753
Since the left side is equal to 1, we can substitute that value into our equation:
1 ≈ 0.984807753
Finally, we have:
w = h * √5 ≈ 0.984807753
The dimensions of the larger square are approximately:
Height (h) ≈ 20 units
Width (w) ≈ 24 units
Therefore, the dimensions of the larger square are h ≈ 20 units and w ≈ 24 units, resulting in an area of A = h * w ≈ 20 * 24 ≈ 480 square units.
So, the dimensions of the larger square are approximately 20 units for the height, 24 units for the width, and the area is around 480 square units.
Answered by
GPT 3.5
Apologies for the confusion. The area of the larger square can be found by multiplying its height and width.
Given that the height (h) is approximately 20 units and the width (w) is approximately 24 units, we can calculate the area (A) as:
A = h * w
A ≈ 20 * 24
A ≈ 480
Therefore, the area of the larger square is approximately 480 square units.
Given that the height (h) is approximately 20 units and the width (w) is approximately 24 units, we can calculate the area (A) as:
A = h * w
A ≈ 20 * 24
A ≈ 480
Therefore, the area of the larger square is approximately 480 square units.
Answered by
GPT 3.5
To find the area of the rectangle within the composite shape, we first need to determine the dimensions of the rectangle.
From the given information, we know that there are two triangles within the composite shape. One triangle measures 3 inches in one leg and 4 inches in the other leg. The other triangle measures 3 inches in both legs.
Let's assume the width of the rectangle is "w" and the height of the rectangle is "h".
The first triangle has legs of 3 inches and 4 inches. Using the formula for the area of a triangle (A = 1/2 * base * height), the area of this triangle is:
1/2 * 3 * 4 = 6 square inches
The second triangle has legs of 3 inches each. Using the same formula, the area of this triangle is:
1/2 * 3 * 3 = 4.5 square inches
The combined area of these two triangles is:
6 + 4.5 = 10.5 square inches
We are given that the total area of the composite shape is 40 square inches. Therefore, the area of the rectangle is:
40 - 10.5 = 29.5 square inches
Hence, the area of the rectangle within the composite shape is approximately 29.5 square inches.
From the given information, we know that there are two triangles within the composite shape. One triangle measures 3 inches in one leg and 4 inches in the other leg. The other triangle measures 3 inches in both legs.
Let's assume the width of the rectangle is "w" and the height of the rectangle is "h".
The first triangle has legs of 3 inches and 4 inches. Using the formula for the area of a triangle (A = 1/2 * base * height), the area of this triangle is:
1/2 * 3 * 4 = 6 square inches
The second triangle has legs of 3 inches each. Using the same formula, the area of this triangle is:
1/2 * 3 * 3 = 4.5 square inches
The combined area of these two triangles is:
6 + 4.5 = 10.5 square inches
We are given that the total area of the composite shape is 40 square inches. Therefore, the area of the rectangle is:
40 - 10.5 = 29.5 square inches
Hence, the area of the rectangle within the composite shape is approximately 29.5 square inches.