Geometry Basics: Oblique Lines, Angles, Shapes and Area

Geometry starts with lines. A horizontal line runs straight across, a vertical line straight up and down, and an oblique line is any line that slants — neither horizontal nor vertical. From lines come angles, shapes, perimeter and area, which these lessons cover step by step.

6 articles

1 min read
The Pythagorean theorem
How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.
1 min read
Area of common shapes and circles
Area formulas for rectangles, triangles, trapeziums and circles — and why the triangle formula has a half in it.
2 min read
Area of a trapezium (trapezoid): formula and examples
The formula for the area of a trapezium (a trapezoid in the US), why it works, and worked examples — including finding a missing height or side.
2 min read
Types of triangles: scalene, isosceles and equilateral
Scalene, isosceles and equilateral triangles — how to tell them apart, their angles, and how to find their area, including the area of an equilateral triangle.
1 min read
Polygons and quadrilaterals: is a square a quadrilateral?
Is a square a quadrilateral? Yes — and a rectangle, a rhombus and a parallelogram. How the family fits together, plus polygon angle sums and areas.
1 min read
Triangular prism volume, cylinders, cones and other 3D shapes
How to find the volume and surface area of a triangular prism, and the volume of cylinders and cones — one idea (area of the cross-section × length) behind most of them.

Horizontal, vertical and oblique lines

Horizontal line: slope 0, equation $y = c$ .
Vertical line: undefined slope, equation $x = c$ .
Oblique line: any other line, such as $y = 2x + 1$ — its slope is a non-zero number.
An oblique line segment is the part of an oblique line between two endpoints, such as the diagonal of a rectangle.

Perimeter vs area

Is perimeter length times width? No — that is the area of a rectangle. Perimeter is the distance around the outside: $P = 2(l + w)$ . Area is the space inside: $A = l \times w$ .

For a rectangle 5 cm by 3 cm, the perimeter is $2(5 + 3) = 16$ cm and the area is $5 \times 3 = 15\text{ cm}^2$ .

Example: the area of a penny

A US one-cent coin is 0.75 inches (19.05 mm) across, so its radius is 0.375 inches. Its area is $\pi r^2 = \pi \times 0.375^2 \approx 0.442$ square inches, or about $2.85\text{ cm}^2$ .

Frequently asked questions

What is an oblique line?

A straight line that is neither horizontal nor vertical — it slants. Its slope is a number other than 0, such as 2 or $-\frac{1}{3}$ .

Is perimeter length times width?

No. Length times width is the area of a rectangle. The perimeter adds all four sides: $2 \times (\text{length} + \text{width})$ .

Which geometry formulas should I know first?

Perimeter and area of rectangles and triangles, the circumference and area of a circle, and Pythagoras’ theorem for right triangles.

Geometry Basics: Oblique Lines, Angles, Shapes and Area

The Pythagorean theorem

Area of common shapes and circles

Area of a trapezium (trapezoid): formula and examples

Types of triangles: scalene, isosceles and equilateral

Polygons and quadrilaterals: is a square a quadrilateral?

Triangular prism volume, cylinders, cones and other 3D shapes