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ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD?
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ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find ...
**Solution:**
Given that ABCD is a parallelogram and X and Y are the midpoints of BC and CD respectively. We need to find the ratio of the area of triangle AXY to the area of parallelogram ABCD.
**Step 1: Determine the properties of a parallelogram**
A parallelogram is a quadrilateral in which opposite sides are parallel and equal in length.
**Step 2: Determine the properties of a triangle**
A triangle is a polygon with three sides and three angles. The area of a triangle is given by the formula: Area = 1/2 * base * height.
**Step 3: Determine the properties of a mid-segment**
A mid-segment is a line segment that connects the midpoints of two sides of a triangle. In this case, X is the midpoint of BC and Y is the midpoint of CD.
**Step 4: Determine the properties of a mid-segment in a parallelogram**
In a parallelogram, the mid-segment is equal in length to half the length of the base. Therefore, the length of segment XY is equal to half the length of segment BC.
**Step 5: Determine the ratio of the area of triangle AXY to the area of parallelogram ABCD**
Since XY is a mid-segment, it divides the parallelogram ABCD into two congruent triangles, AXB and YXC.
The area of triangle AXY is given by the formula: Area = 1/2 * base * height. In this case, the base is XY and the height is the perpendicular distance from A to XY.
The area of parallelogram ABCD is given by the formula: Area = base * height. In this case, the base is AB and the height is the perpendicular distance from A to AB.
Since XY is a mid-segment, it is equal in length to half the length of BC. Therefore, XY = BC/2.
Since XY is parallel to AB, the perpendicular distance from A to XY is equal to the perpendicular distance from A to AB.
Therefore, the ratio of the area of triangle AXY to the area of parallelogram ABCD is:
Area of triangle AXY/Area of parallelogram ABCD = (1/2 * XY * height)/(AB * height)
= 1/2 * (BC/2) * height/(AB * height)
= 1/4 * BC/AB
Therefore, the ratio of the area of triangle AXY to the area of parallelogram ABCD is 1/4.
In conclusion, the ratio of the area of triangle AXY to the area of parallelogram ABCD is 1/4.
Given that ABCD is a parallelogram and X and Y are the midpoints of BC and CD respectively. We need to find the ratio of the area of triangle AXY to the area of parallelogram ABCD.
**Step 1: Determine the properties of a parallelogram**
A parallelogram is a quadrilateral in which opposite sides are parallel and equal in length.
**Step 2: Determine the properties of a triangle**
A triangle is a polygon with three sides and three angles. The area of a triangle is given by the formula: Area = 1/2 * base * height.
**Step 3: Determine the properties of a mid-segment**
A mid-segment is a line segment that connects the midpoints of two sides of a triangle. In this case, X is the midpoint of BC and Y is the midpoint of CD.
**Step 4: Determine the properties of a mid-segment in a parallelogram**
In a parallelogram, the mid-segment is equal in length to half the length of the base. Therefore, the length of segment XY is equal to half the length of segment BC.
**Step 5: Determine the ratio of the area of triangle AXY to the area of parallelogram ABCD**
Since XY is a mid-segment, it divides the parallelogram ABCD into two congruent triangles, AXB and YXC.
The area of triangle AXY is given by the formula: Area = 1/2 * base * height. In this case, the base is XY and the height is the perpendicular distance from A to XY.
The area of parallelogram ABCD is given by the formula: Area = base * height. In this case, the base is AB and the height is the perpendicular distance from A to AB.
Since XY is a mid-segment, it is equal in length to half the length of BC. Therefore, XY = BC/2.
Since XY is parallel to AB, the perpendicular distance from A to XY is equal to the perpendicular distance from A to AB.
Therefore, the ratio of the area of triangle AXY to the area of parallelogram ABCD is:
Area of triangle AXY/Area of parallelogram ABCD = (1/2 * XY * height)/(AB * height)
= 1/2 * (BC/2) * height/(AB * height)
= 1/4 * BC/AB
Therefore, the ratio of the area of triangle AXY to the area of parallelogram ABCD is 1/4.
In conclusion, the ratio of the area of triangle AXY to the area of parallelogram ABCD is 1/4.
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ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find ...
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ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD?
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ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD?.
ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a parallelogram.X and Y are the mid- points of BC and CD.Find the ratio of ar ( /_AXY ) to ar ( |gm ABCD?.
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