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neurologyYou need to know

• Perimeter is the total distance around the outside of a two-dimensional shape, measured in units such as cm or m.
• Area is the amount of surface inside a two-dimensional shape, measured in square units such as `cm^2` or `m^2`.
• The perimeter of a polygon drawn on a square grid can be found by counting the unit lengths around its outside edge.
• The area of a polygon drawn on a square grid can be found by counting full squares and combining part-squares to make whole squares.
• The area of a rectangle is found using `area = length \times width`.
• The area of a triangle is found using `area = \frac{1}{2} \times base \times height`, where the height is perpendicular to the base.
• The area of a parallelogram is found using `area = base \times perpendicular\ height`.
• A compound shape is a shape made from two or more basic shapes joined together.
• The perimeter of a compound shape is found by adding only the lengths around the outside boundary of the shape.
• The area of a trapezium is found using `area = \frac{1}{2}(a+b)h`, where `a` and `b` are the parallel sides and `h` is the perpendicular height.
• The circumference of a circle is the distance around the circle and is found using `circumference = \pi d` or `circumference = 2\pi r`.
• The area of a circle is found using `area = \pi r^2`, where `r` is the radius.
• A semicircle is half of a circle, so its area is `\frac{1}{2}\pi r^2` and its curved arc length is `\frac{1}{2}\times 2\pi r`.
• A quarter-circle is one quarter of a circle, so its area is `\frac{1}{4}\pi r^2` and its curved arc length is `\frac{1}{4}\times 2\pi r`.
• Volume is the amount of three-dimensional space inside a solid, measured in cubic units such as `cm^3` or `m^3`.
• The volume of a cuboid is found using `volume = length \times width \times height`.
• The volume of a prism is found using `volume = area\ of\ cross\text{-}section \times length`.
• A cylinder is a prism-like solid with a circular cross-section, and its volume is found using `volume = \pi r^2 h`.
• Surface area is the total area of all the faces of a three-dimensional solid, measured in square units.
• The surface area of a prism is found by adding the areas of all its faces, including the two congruent cross-sections and the rectangular side faces.

• Calculate the perimeter of a polygon on a square grid by counting each unit length around the outside exactly once.
• Calculate the area of a grid-based polygon by counting full squares and combining matching part-squares to make whole squares.
• Calculate the area of rectangles, triangles, parallelograms and trapezia by selecting the correct formula and using the perpendicular height where required.
• Find the perimeter of a compound shape by identifying any missing side lengths and adding only the exterior side lengths.
• Calculate the area of a compound shape by splitting it into basic shapes, finding each area, and adding or subtracting areas as appropriate.
• Calculate the area and circumference of circles and part-circles by substituting the correct radius or diameter into the circle formulae and including straight edges when finding perimeter.
• Calculate the volume of cubes, cuboids, triangular prisms and other prisms by finding the cross-sectional area and multiplying by the prism length.
• Calculate the volume of a cylinder by finding the circular cross-sectional area and multiplying by the height.
• Calculate the surface area of cuboids and triangular prisms by finding the area of every face and adding the areas without duplication.