Mensuration and trigonometry Study Guide

Perimeter is the total distance around the outside boundary of a shape. For a composite shape, trace the boundary once, include every outside edge, calculate any missing lengths from aligned totals, and exclude internal joining lines. All lengths must use the same unit.

On an L-shape, a missing horizontal step can be found by subtracting known horizontal parts from the total width; the same idea applies vertically. Then add only the exterior segments. A reliable check is that total rightward length equals total leftward length, and total upward length equals total downward length.

A strong solution states the relevant rule, substitutes or transforms values carefully, shows intermediate reasoning, and checks that the result is reasonable and in the required form. Common errors come from omitted terms, mishandled signs, premature rounding or using a rule that does not match the structure of the problem.

The area of a triangle is the amount of two-dimensional space it covers. Unlike squares and rectangles where you multiply length by width, triangles have a slightly different formula. Think about a rectangle or a parallelogram: If you cut it diagonally from one corner to the opposite, you create two identical triangles. This observation is key to understanding the formula for a triangle's area.

The formula for the area of a triangle is given by: Area = (1/2) × base × height. Let's break down what 'base' and 'height' mean in this context.

The 'base' can be any side of the triangle. Often, it's the side that the triangle appears to rest on. The 'height' (also called the perpendicular height or altitude) is the perpendicular distance from the chosen base to the opposite vertex (corner) of the triangle. It's crucial that the base and height are perpendicular to each other, meaning they meet at a 90-degree angle. If the height isn't immediately obvious, you might need to draw an imaginary line from the vertex to the base, ensuring it forms a right angle. For some triangles (like obtuse triangles), the perpendicular height might fall outside the triangle itself; in such cases, the base needs to be extended to meet the perpendicular height line.

To calculate the area, you simply multiply the base by the height and then divide the result by two (or multiply by 0.5). Always remember to state your answer in square units, such as cm², m², or mm².