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neurologyYou need to know

• A trapezium has exactly one pair of parallel sides in GCSE geometry contexts.
• The area of a trapezium is `\frac{1}{2}(a+b)h`, where `a` and `b` are the parallel side lengths and `h` is the perpendicular distance between them.
• A compound shape is made from two or more simpler shapes, such as rectangles, triangles, trapezia, circles or part-circles.
• The area of a compound shape can be found by adding the areas of its non-overlapping parts or by subtracting missing areas from a larger shape.
• A semi-circle is half of a circle, so its area is `\frac{1}{2}\pi r^2` and its curved arc length is `\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}{2}\pi r`.
• The perimeter of a part-circle includes both the curved arc and any straight edges, such as a diameter or radii.
• A prism is a 3D solid with a constant cross-section along its length.
• The volume of any prism is `\text{area of cross-section} \times \text{length}`.
• A triangular prism has a triangular cross-section, so its volume is `\text{area of triangle} \times \text{length}`.
• A cylinder is a prism-like solid with a circular cross-section.
• The volume of a cylinder is `\pi r^2h`, where `r` is the radius of the circular cross-section and `h` is the perpendicular height or length.
• Surface area is the total area of all the outside faces of a 3D solid.
• The surface area of a cuboid is `2lw+2lh+2wh`, where `l`, `w` and `h` are its length, width and height.
• The surface area of a prism is found by adding the areas of its two identical end faces and all its rectangular side faces.
• The curved surface area of a cylinder is `2\pi rh`, because the curved face unwraps to a rectangle with width equal to the circumference `2\pi r` and height `h`.
• The total surface area of a closed cylinder is `2\pi r^2+2\pi rh`.
• For a sector with central angle `\theta` degrees, the arc length is `\frac{\theta}{360}\times 2\pi r` and the sector area is `\frac{\theta}{360}\times \pi r^2`.
• A circular segment is the region between a chord and an arc, and the area of a minor segment is found by subtracting the isosceles triangle area from the sector area.
• Area is measured in square units, volume is measured in cubic units, and perimeter, arc length and length are measured in linear units.

• Calculate the area of a trapezium by identifying the two parallel sides and the perpendicular height, then substituting into `\frac{1}{2}(a+b)h`.
• Calculate the area of a compound shape by splitting it into simple non-overlapping shapes or subtracting missing regions, showing each area before combining them.
• Calculate the perimeter and area of semi-circles and quarter-circles by using the correct fraction of the circle and including any straight edges in the perimeter.
• Calculate the volume of complex prisms by finding the cross-sectional area accurately and multiplying it by the prism length.
• Calculate the volume of a cylinder by identifying the radius and perpendicular height, then using `\pi r^2h` with suitable units.
• Calculate the surface area of cuboids, triangular prisms and other prisms by drawing or imagining the net and adding the areas of every outside face once.
• Calculate the total surface area of a cylinder by adding the areas of the two circular ends and the curved surface area.
• Calculate the length of any arc by using the fraction `\frac{\theta}{360}` of the full circumference.
• Calculate the area of a circular segment by finding the sector area, finding the area of the triangle formed by the two radii and the chord, and subtracting the triangle from the sector for a minor segment.