Geometry Problems

Understanding Perimeter and Area

Define perimeter as the total distance around the boundary of a 2D shape.
Recall that to calculate the perimeter of a rectangle, multiply the length by 2 and add it to the width multiplied by 2: 2l + 2w
Define area as the amount of space within the boundary of a 2D shape.
Remember that to calculate the area of a rectangle, multiply the length by the width: lw
Understand that for a triangle, the formula for area is 1/2 multiplied by base multiplied by height: 1/2bh

Identify a circle as a set of points in a plane that are equidistant from a central point.
Recall the formula for the circumference of a circle: 2πr, where ‘r’ is the radius.
Understand the formula for the area of a circle: πr²
Note that diameter is twice the radius: d = 2r

Recall Pythagoras’s theorem: in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Express this as the formula a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Define trigonometry as the branch of mathematics dealing with the relations of the sides and angles of triangles.
Understand the three basic trigonometric ratios - sine (sin), cosine (cos) and tangent (tan).
Recall the SOHCAHTOA mnemonic to remember these ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Apply these ratios to solve problems involving right-angled triangles.

Recognise common 3D shapes such as cubes, cuboids, cylinders, cones, spheres, and pyramids.
Understand that the volume of a cuboid can be calculated by the formula length × width × height.
Know that the volume of a cylinder is given by the formula πr²h, where r is the radius of the base and h is the height of the cylinder.
Recall that the volume of a cone is 1/3 times the area of the base times the height: 1/3πr²h
Remember that the volume of a sphere is given by the formula 4/3πr³, with r being the radius of the sphere.