,
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- sides of a triangle
- semiperimeter
- semi-major axis
- semi-minor axis
3,14
- height measured at right angles to the base
- equal sides
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- sides of a scalene triangle
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- angles
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- sides of a scalene triangle
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- angles
1. The area of a rhombus if you know diagonals and angle
- larger diagonal
- smaller diagonal
- acute angle
- obtuse angle
2. The area of a rhombus if you know side and angle
- side
,
- angles
3. The area of a rhombus if you know side and radius of the inscribed circle
- side
- height
- radius of the inscribed circle
1. The area of a parallelogram if you know sides and angle
,
- sides
,
- angles
2. How to find the area of a parallelogram if you know side(base) and height
,
- sides - base
- height measured at right angles to the side
- height measured at right angles to the side
3. The area of a parallelogram if you know diagonals and angle between them
,
- diagonals
,
- angles between the diagonals
- length of a rectangle
- width of a rectangle
- side
- diagonal
1. How to find the area of a trapezoid (called a trapezium in the UK) if you know bases, height and middle line of a trapezoid
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- bases
- height
- area of a trapezoid
2. How to find the area of a trapezoid (trapezium UK) if you know diagonals and angle between them
,
- diagonals
,
- angles between the diagonals
- area of a trapezoid
3. How to find the area of a trapezoid (trapezium UK) if you know all sides
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,
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- sides
- area of a trapezoid
Definition of a trapezoid (also known as trapezium)
Trapezoid is a quadrilateral in which only one pair of opposite sides are parallel
Properties of a trapezoid (trapezium UK)
1. The middle line of the trapezoid is parallel to the bases and is equal to their half-sum.
2. The bisector of any angle of the trapezoid cuts off on its base (or continuation) an interval equal to the leg.
3. The triangles , formed by segments of the diagonals and the bases of the trapezoid, are similar.
4. Triangles formed by segments of the diagonals and the leg of the trapezoid, have the same area.
5. A circle can be inscribed into a trapezoid if the sum of the bases of the trapezoid is equal to the sum of its lateral sides.
6. The segment connecting the midpoints of the diagonals is equal to the half-difference of the bases and lies on the midline.
7. The intersection point of the diagonals of the trapezoid, the point of intersection of the extensions of its lateral sides and the middle of the bases lie on one straight line.
8. If the sum of the angles at any base of the trapezoid is 90 °, then the segment connecting the midpoints of the bases is equal to their half-difference.
1. The area of an isosceles trapezoid if you know sides and angle
- lower base
- upper base
- equal lateral sides
- angle at the lower base
2. The area of an isosceles trapezoid in the case of a circle being inscribed in it
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- bases of an isosceles trapezoid
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- angles of an isosceles trapezoid
- radius of the inscribed circle
- diameter of the inscribed circle
- center of the inscribed circle
- height
3. The area of an isosceles trapezoid in the case of a circle being inscribed in it and if you know middle line
,
- bases of an isosceles trapezoid
- equal lateral sides
- radius of the inscribed circle
- center of the inscribed circle
4. The area of a isosceles trapezoid if you know diagonals and angle between them
- diagonal of a trapezoid
,
- angles between the diagonals
5. The area of an isosceles trapezoid if you know lateral side, middle line and angle
- equal lateral sides
- middle line
,
- angles at the bases
6. The area of an isosceles trapezoid if you know bases and height
,
- bases of an isosceles trapezoid
- height measured at right angles to the base
- side
- number of sides
- radius
- diameter
3,14
- radius
- length of the arc AB
- angle of the sector AOB
3,14
- radius
- angle of the segment
3,14
- radius of the outer circle
- radius of the inner circle
3,14
- radius of the outer circle
- radius of the inner circle
- angle of the sector AOB
3,14
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- legs of a right triangle
- height measured at right angle to the base
- base