This document provides definitions and formulas for calculating perimeters, areas, volumes, and other measurements for basic geometric shapes including triangles, squares, rectangles, pentagons, prisms, cylinders, pyramids, and cones. It defines key terms like perimeter, area, volume, lateral area, surface area, base, height, slant height, axis, and more. Formulas are provided for calculating these values for each type of shape.

1. MATH Project
Hoor yahya ali
9 – 2 E

2. 6) What is the unit for perimeter? inches, feet, yards, or miles.
Perimeter :
1) What is a perimeter? A perimeter is a path that encompasses/surrounds a two-dimensional shape
2) What is the perimeter of a triangle? P= a + b + c
5) What is the perimeter of a square?P=4a
3) What is the perimeter of a Rectangle ? P= 2 (L+W)
4) What is theperimeterof a five sidedfigure? P=5s

3. Area :
1) What is area? the quantity that expresses the extent of a two-dimensional figure or shape or planar
lamina, in the plane.
2) What is the areaof a triangle? A= ½ bh
5) What is the unit for area ? Square units
3) What is the areaof a square?A= a^2
4) What is theperimeterof rectangle ? A= wh

4. Volume :
1) What is volume ? the quantity of three-dimensional space enclosed by a closed surface
2) What is the unit for Volume? cubic units

5. 5) What is the unit for Surface Area? square units
Lateral Area andSurface Area :
1) What is Lateral Area? the area of all the sides of the object, excluding the area of its base and top.
2) What is Lateral Face and Lateral Edge? A lateral edge is the intersection of two lateral faces, Lateral faces are
the faces in a prism or pyramid that are not bases.
3) What is Surface Area? The surface area of a solid object is a measure of the total area that the surface of the
object occupies.
4) What is theunit for Lateral Area?square units

6. 6) WhatistheLateralAreaof a Prism?When a prismhas its bases facing up and down, the lateralareais the areaof the vertical faces.
Prism:
1) Whatisa polyhedron? a three-dimensional solid which consists of a collection of polygons, usually joined at their edges.
2) Whatis a Prism? a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy of the first, and n
other faces joining corresponding sides of the two bases.
5) Whatis altitude(height)of a Prism? a segment with one endpoint in one of the bases, the other endpoint in the plane that contains the
other base, perpendicular to that base.
3) Whatis a rightPrism? a geometric solid that has a polygon as its base and vertical sides perpendicular to the base.
4) WhatisanobliquePrism? a prism in which the bases are parallel, but one is not directly over the other, and all lateral faces are
parallelograms.
7) WhatistheSurfaceAreaof a Prism? T. S. A. =ph+2B where p represents the perimeter of the base, h the height of
the prism and B the areaof the base.
8) WhatistheVolumeof a Prism? V=Bh , where B is the base area and h is the height.

7. 7) What is the Volume of a Cylinder? V=πr2h
Cylinder:
1) What is a cylinder ? a closed solid that has two parallel (usually circular) bases connected by a curved
surface.
2) What is the axis of a Cylinder? the segment containing the centers of the two bases.
6) What is the Surface Areaof a Cylinder? A=2πrh+2πr^2
4) What is an oblique Cylinder?is one that 'leans over' - where the sides are not perpendicular to the
bases. Opposite of a 'right cylinder'.
5) What is the Lateral Areaof a Cylinder? AL=2πrh
3) What is a right Cylinder? the segment containing the centers of the two bases.

8. 6) WhatistheLateralAreaof a Pyramid?AL = (perimeter of base × slant height of pyramid) ÷ 2
Pyramid:
1) Whatisa pyramid? a structure whose outer surfaces are triangular and converge to a single step at the top, making the
shape roughly a pyramid in the geometric sense.
2) Whatis a regularPyramid? a right pyramid whose base is a regular polygon.
5) Whatis Slantheight? the distance measured along a lateral face from the base to the apex along the "center" of the face.
3) Whatis a NonregularPyramid?A non-regular pyramid does not have a slant height.
4) Whatisthevertexof a pyramid?the point that is part of all the lateral faces, or where all the lateral edges meet.
7) WhatistheSurfaceAreaof a Pyramid? start by multiplying the perimeter of the pyramid by its slant height. Then, divide that number
by 2. Finally, add the number you get to the area of the pyramid's base to find the surface area.
8) WhatistheVolumeof a Pyramid? findthe length and width of the base, then multiple those numbers together to determinethe area of the
base. Next, multiply the area of the base by the height of the pyramid. Take that result and divide it by 3 to calculate the pyramid'svolume

9. 7) What is the Volume of a Cone?V=π r ^ 2 ×h / 3
Cone:
1) What is a cone ? a three-dimensional geometric shape that tapers smoothly from a flat base to a point called
the apex or vertex.
2) What is the axis of a Cone? the segment whose endpoints are the vertex and the center of the base.
6) What is the Surface Areaof a Cone? the curved surface area plus the area of the base: π r 2 + π L r , pi r^2 + pi L r,
πr2+πLr, where r denotes the radius of the base of the cone, and L denotes the slant height of the cone. The
curved surface area is also called the lateral area.
4) What is an oblique Cone?A cone with an apex that is not aligned above the center of the base.
5) What is the Lateral Areaof a Cone? L. S. A=πrl , where l is the slant height of the cone .
3) What is a right Cone?A cone that has its apex aligned directly above the center of its base. The base need
not be a circle.