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neurologyYou need to know

• Area measures the amount of surface inside a 2D shape and is written in square units such as `\text{cm}^2` or `\text{m}^2`.
• Perimeter measures the total distance around the outside of a 2D shape and is written in linear units such as `\text{cm}` or `\text{m}`.
• Volume measures the space inside a 3D solid and is written in cubic units such as `\text{cm}^3` or `\text{m}^3`.
• Surface area is the total area of all the outside faces or curved surfaces of a 3D solid and is written in square units.
• The area of a rectangle is `l \times w`, where `l` is the length and `w` is the width.
• The area of a triangle is `\frac{1}{2}bh`, where `b` is the base and `h` is the perpendicular height.
• The area of a circle is `\pi r^2`, where `r` is the radius.
• The circumference of a full circle is `2\pi r`, which is also equal to `\pi d`.
• The area of a semicircle is half the area of a full circle, so it is `\frac{1}{2}\pi r^2`.
• The perimeter of a semicircle is not just the curved part; it is the half-circumference plus the diameter, so it is `\pi r + 2r`.
• The radius is half the diameter, so if the diameter is known then `r = \frac{d}{2}`.
• A compound shape is made from two or more simple shapes, so its area can be found by adding or subtracting the areas of those parts.
• A prism has the same cross-section all the way through its length, so its volume is `\text{area of cross-section} \times \text{length}`.
• A cylinder is a prism with a circular cross-section, so its volume is `\pi r^2 h`, where `h` is the perpendicular height.
• The surface area of a cube with edge length `a` is `6a^2` because it has six congruent square faces.
• The surface area of a cuboid with length `l`, width `w`, and height `h` is `2lw + 2lh + 2wh`.
• All lengths must be in the same unit before calculating area, perimeter, surface area, or volume.
• When a calculation involves `\pi`, answers may be left exactly in terms of `\pi` or given as a decimal approximation, depending on the question.

• Decompose a compound shape into simple parts such as rectangles, triangles, and semicircles, then add or subtract their areas accurately.
• Calculate the area of a semicircle by finding the radius, substituting into `\frac{1}{2}\pi r^2`, and giving the answer in square units.
• Calculate the perimeter of a semicircle by working out the half-circumference and then adding the diameter.
• Find the volume of a complex prism by calculating the area of its constant cross-section and multiplying by the prism length.
• Calculate the volume of a cylinder by finding the area of the circular base and multiplying by the perpendicular height.
• Calculate the surface area of a cube by finding the area of one square face and multiplying by 6.
• Calculate the surface area of a cuboid by finding the areas of the three different face pairs and summing them as `2lw + 2lh + 2wh`.
• Convert measurements into consistent units before substituting into a formula, then label the final answer with the correct linear, square, or cubic units.
• Use a diagram or net to identify missing lengths, radii, diameters, faces, and cross-sections before carrying out calculations.
• Present answers involving `\pi` correctly by leaving them in exact form or rounding a decimal answer to the accuracy requested.