Area: Triangle

Learn how to calculate the area of any triangle using the base and height, and practice dynamic exercises.

Triangle

Use the workspace below. Write equations like A = 30 to solve for the area.

Learning Topics

📖 Area Study Guide

1. Base and Height of a Triangle

To calculate the area of any triangle, we need two key measurements:
• Base (b): Any of the triangle's three sides.
• Height (h): The perpendicular line segment from the opposite vertex to that base (or its extension). The height is always at a 90° angle to the base.

Height of a Triangle

The height of a triangle relative to a base is the perpendicular distance from that base (or its extension) to the opposite vertex.

Acute Triangle

An acute triangle is a triangle where all three interior angles are acute (each less than

90^\circ

Acute Triangle (Height Inside)

In an acute triangle (where all angles are less than 90°), the height to the base falls inside the triangle.

Obtuse Triangle

An obtuse triangle is a triangle that has one interior angle that is obtuse (greater than

90^\circ

Obtuse Triangle (Height Outside)

In an obtuse triangle (where one angle is greater than 90°), the height to the base can fall outside the triangle. To measure it, we extend the base line outwards.

2. Intersection of Heights (Orthocenter)

Every triangle has three heights (one for each of its three sides). An elegant property of geometry is that all three heights (or their extensions) intersect at exactly one point. This intersection point is called the orthocenter.

3. Triangle Area Formula

Since any triangle is exactly half of a parallelogram (or rectangle) with the same base and height, its area is given by multiplying the base and height and dividing by 2:

A = \frac{b \times h}{2}

Where:
•

b

is the length of the base (opposite side).
•

h

is the height perpendicular to that base.

Area of a Triangle

A = \frac{b \times h}{2}

Frequently Asked Questions

How do you calculate the area of a general triangle?

The area of any general triangle is calculated as half the base times the height (A = (1/2) × b × h or A = bh/2), where the height is the perpendicular distance from the base to the opposite vertex.

How do you calculate the area of a right-angled triangle?

The area of a right-angled triangle is calculated by multiplying its two perpendicular legs and dividing by 2 (A = ab / 2). This is because a right-angled triangle is exactly half of a rectangle with the same width and height.

What are the main types of special triangles?

The three main types are: isosceles (two equal sides and two equal base angles), equilateral (all sides and angles equal — each angle is 60°), and the 30-60-90 right triangle (fixed side ratios of 1 : √3 : 2).