Key Points

The area of a trapezium is calculated as half the product of its height and the sum of its parallel sides. The formula is $A = \frac{1}{2} \times h \times (a+b)$, where $h$ is the height, and $a$ and $b$ are the lengths of the parallel sides.

To find the area of a general quadrilateral, divide it into two triangles using one of its diagonals. The area is $A = \frac{1}{2} \times d \times (h_1 + h_2)$, where $d$ is the length of the diagonal, and $h_1$ and $h_2$ are the perpendicular heights from the opposite vertices to that diagonal.

The area of a rhombus is half the product of the lengths of its diagonals. The formula is $A = \frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the two diagonals.

The Total Surface Area (TSA) of a cuboid is the sum of the areas of its six rectangular faces. The formula is $TSA = 2(lb + bh + hl)$, where $l$ is length, $b$ is breadth, and $h$ is height.

The Lateral Surface Area (LSA) of a cuboid is the area of its four side faces (excluding the top and bottom). The formula is $LSA = 2h(l+b)$, where $l$ is length, $b$ is breadth, and $h$ is height.

A cube has six identical square faces. Its Total Surface Area (TSA) is given by the formula $TSA = 6a^2$, where $a$ is the length of one edge.

The Lateral Surface Area (LSA) of a cube is the area of its four side faces. The formula is $LSA = 4a^2$, where $a$ is the length of one edge.

The Curved Surface Area (CSA) of a right circular cylinder is the area of its curved surface. The formula is $CSA = 2\pi rh$, where $r$ is the radius of the base and $h$ is the height.

The Total Surface Area (TSA) of a cylinder is the sum of its curved surface area and the areas of its two circular bases. The formula is $TSA = 2\pi r(r+h)$, where $r$ is the radius and $h$ is the height.

The volume of a cuboid is the product of its length, breadth, and height. The formula is $V = l \times b \times h$. Volume is measured in cubic units like $\text{cm}^3$ or $\text{m}^3$.

The volume of a cube is found by cubing the length of its edge. The formula is $V = a^3$, where $a$ is the length of the edge.

The volume of a cylinder is the product of the area of its circular base and its height. The formula is $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.

Volume measures the space an object occupies, while capacity is the amount a container can hold. Key conversions to remember are $1 \text{ L} = 1000 \text{ cm}^3$ and $1 \text{ m}^3 = 1000 \text{ L}$.

To find the area of an irregular polygon, divide the polygon into simpler shapes like triangles, rectangles, or trapeziums. Calculate the area of each individual shape and then sum them up to find the total area of the polygon.