Geometric Shapes

Geometric shapes are figures that are defined by their shape and size. These shapes can be divided into two-dimensional (2D) and three-dimensional (3D) shapes.

Two-Dimensional (2D) Shapes

Two-dimensional shapes are flat, and they can be measured in terms of length and width. Some common 2D shapes include:

Three-Dimensional (3D) Shapes

Three-dimensional shapes have length, width, and height. Some common 3D shapes include:

Geometric Formulas

There are various formulas associated with geometric shapes. Some important formulas to remember include:

Area Formulas

The area of a shape is the amount of space inside the shape. Here are the area formulas for some common 2D shapes:

Circle: A = πr² (where π is pi and r is the radius)
Square: A = s² (where s is the length of a side)
Rectangle: A = l * w (where l is the length and w is the width)
Triangle: A = 0.5 * b * h (where b is the base and h is the height)

Volume Formulas

The volume of a shape is the amount of space it occupies. Here are the volume formulas for some common 3D shapes:

Sphere: V = (4/3)πr³ (where π is pi and r is the radius)
Cube: V = s³ (where s is the length of a side)
Cylinder: V = πr²h (where π is pi, r is the radius, and h is the height)
Rectangular prism: V = lwh (where l is the length, w is the width, and h is the height)

Geometric Properties

Geometric shapes also have various properties that define them. Some important properties to remember include:

A circle has 360 degrees.
The sum of angles in a triangle is 180 degrees.
The sum of angles in a quadrilateral is 360 degrees.
Opposite sides of a rectangle or square are equal in length.
A cube has 6 faces, 12 edges, and 8 vertices.

Study Guide

When studying geometric shapes, make sure to:

Memorize the formulas for finding the area and volume of different shapes.
Practice identifying and drawing different geometric shapes.
Understand the properties and characteristics of each shape.
Work on problems that involve calculating the area, volume, and angles of geometric shapes.
Use visual aids such as diagrams and models to help understand the concepts better.

By mastering these concepts, you'll be well-prepared to tackle geometric problems and understand the role of shapes in the world around you.

◂Math Worksheets and Study Guides Seventh Grade. Geometric Proportions

Study Guide

Geometric Proportions

Worksheet/Answer key

Geometric Proportions

Worksheet/Answer key

Geometric Proportions

Worksheet/Answer key

Geometric Proportions

Worksheet/Answer key

Numerical & Geometric Proportions

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.