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Rotations preserve distance, angle measures, and orientations of figures. The points move around the origin.

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The volume of a prism can be determined by multiplying the area of the base times the height of the prism, or V=Bh. The same goes for the cylinder, except the equation can also be written as V=piR²h.

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Carson Coffman-10.4 Continued

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You can use ratios to compare the perimeters and areas of similar figures. For instance, if the scale factor of two figures is a/b, then
(1) the ratio of their perimeters is a/b and
(2) the ratio of their areas is a^2/b^2.
You can find ratios in similar figures by finding their side lengths. If you want to find the ratio of their areas you square the ratio then simplify.

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The are of a trapezoid can be found by adding both basses and multiplying by the height. Then divide by two. Certain trapezoids can be broken into different shapes and you can add the areas of the figure together. And sometimes you can rearrange the shape to make a rectangle and, just find the area of that.

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Kelly Gillen- 11.5 volumes of cones and pyramids

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Kelly Gillen- 11.5 volumes of cones and pyramids

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The volume of a pyramid is one third the product of the area of the base and the height of the pyramid.
V = 1/3 BH
The volume of a cone is one third the product of the sea of the base and the height of the cone.
V= 1/3 BH or v= 1/3 πr^2h

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You can use trigonometry to find the area of a regular polygon when you know the length of a side, radius, or apothem.

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A pyramid is a polyhedron made up of a polygon base and triangles that intersect at a point. A cone has a circular base and one vertex. To find the surface area of a pyramid or a cone, add the area of the base and the lateral area. To find lateral area of a pyramid, multiply the perimeter of the base and the slant height, and to find the lateral area of a cone, use the formula 3.14(r)(l).

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By Abby, and Nikki
How to find the area of a regular polygon. Each regular polygon is divided into congruent triangles by the radii and by finding the area of these triangles you can find the area as a whole. The formula, 1/2 ap, is taking the area of one triangle and multiplying it by the number of triangles in the polygon. It takes the apothem, which is used to find the area of a triangle, and multiplies it by the perimeter and divides the whole thing in half, which gives you the area of all the triangles added together, or the area of a regular polygon.

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The area of a segment of a circle can be found by subtracting the area of the circle by the area of the triangle in the sector of a circle.

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Circles and Arcs, a circle is set of all points in a plain equidistant form the center. An arc is a segment of the circumference of a circle. The length of an arc is the angle measure of the arc divided 360 multiplied by 2 pi r.

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Similar solids have the same shape and all their corresponding dimensions are proportional. If the scale factor of two similar solids is a:b, then the ratio of their corresponding surface areas is a^2:b^2, and the ratio of their volumes is a^3:b^3.

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A sphere is the set of all points in space equidistant from a given called the center. A radius is a segment that has one endpoint at the center and the other endpoint on the sphere. A diameter is a segment passing through the center with endpoints on the sphere.

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By using the nets of cylinders and prisms, you can find the overall surface area by adding together the areas of the individual shapes in each net. The equation for finding the surface area of a prism is SA= LA (perimeter x height) + 2B (area of a base). The equation for finding the surface area of a cylinder is SA= 2(pi)rh +2(pi)r(squared). To find the height of an oblique figure, use a right triangle from the figure’s base to its top.

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Transformations  of a geometric figure is a function or mapping that results in a change in the position, size, or shape of the figure. You have the pre-image which is the figure before it is changed and the image which is the figure after a transformation.the key concept is about translations and that is when all the points of a figure are mapped the same distance and direction away from the original figure.

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Polyhedrons are made up of faces, edges, and vertices. The relationship between those things is shown in Euler’s formula: F+V=E+2. It also also important to understand that a cross section is the intersection of a solid and a plane, and it’s like a thin slice of the solid. Cross sections have different properties depending on the solid.

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You can use compositions of rigid motions and dilations to help you understand the properties of similarities.

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A Dialation can be written as D(n c) and is an enlargement if the scale factor n is greater than 1 but the dialation is a reduction if the scale factor is between 0and 1. To identify coordinates, use the dialation rule D2(x,y).