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Unit 10 Area: Coggle Mind Map, image, image, image, image, image, image,…
Unit 10 Area: Coggle Mind Map
Sectors and circle
sector of a circle
- is protion of a circle enclosed by two radii and an arc
central angle
- angle the forms when two radii meet at the cetner of the circle
Formula for area of a sector
- (1/2)pi^2 C
Arc angle
-
an arc measure is an angle the arc makes at the center of a circle
Parallelograms and Triangles
base of a triangle : base can be any side, not just the one drawn at the bottom.
height of a parallelogram
the distance between opposite sides of the parallelogram
base of a parallelogram : defined to be any one of the sides of the parallelogram
height of a triangle : use the Pythagorean Theorem, a^2 + b^2 = c^2.
base angle : either of the angles of a triangle that have one side in common with the base.
Formula for area of Triangle A=hbb/
2
Formula for area of parallelogram : A=bh
Regular Polygons
Center of a regular polygon
The point that is equidistant from each vertex or corner.
central angle of a regular polygon
Angle whose vertex is the center and whose rays, or sides, contain the endpoints of a side of the regular polygon.
Apothem of a polygon
A line segment from the center to the midpoint of one of its sides.
radius of a regular polygon
The distance from the center to a vertex
Trapezoids, Rhombi, and Kites
height of a trapezoid
The distance between the two sides is the height.
Formula for area of a trapezoid
Multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
bases of a trapezoid
The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides (if they are not parallel; otherwise there are two pairs of bases).
Formula for area of a rhombi
To calculate the area of a rhombus, the following formula is used:
A = ½ × d1 × d2
Formula for area of a kite
To find the area of a kite using the 2 diagonals, measure the length of the diagonals. Label these 2 lines x and y. Multiply the lengths of x and y, then divide the result by 2 to get the area of the kite.
diagonal of a kite
The intersection of the diagonals of a kite form 90 degree (right) angles.
Transformations
(m/n)^2
, when m is the length of one side and n is the length of the other
Surface Area of Solid
right cone
A cone that has its apex aligned directly above the center of its base.
slant height
The height of a cone from the vertex to the periphery (rather than the centre) of the base.
lateral edge the intersection of two lateral faces
Triangular prism
three-sided prism, made of a triangular base
lateral area finding the area of the sides of a three-dimensional geometric figure.
Rectangular prism
- six faces that are rectangles
- a pyramid with a hexagonal base upon whcih erected six isosceles triangular face and meet at a point
regular pyramid
A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all equal in length.
cylinder
- curved geometric shapes, with the surface formed by the points at a fixed distance from a give line segment
lateral face : the face or surface of a solid on its sides
