Area is a measure of how much space a two-dimensional shape takes up. It is usually measured in square units, such as square meters or square inches.

**1. Rectangles and Squares:** To calculate the area of a rectangle or a square, you multiply the length by the width. The formula for the area (A) of a rectangle is: A = length × width.

**2. Triangles:** The area of a triangle can be calculated using the formula: A = 1/2 × base × height, where the base is the length of the bottom side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

**3. Circles:** The area of a circle can be calculated using the formula: A = πr^{2}, where π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle.

Composite figures are made up of a combination of basic shapes. To find the area of a composite figure, you can divide it into basic shapes, calculate the area of each shape, and then add the areas together.

Here are some important points to remember when studying area:

- Understand the formulas for calculating the area of rectangles, squares, triangles, and circles.
- Practice using these formulas to solve problems involving different shapes and dimensions.
- Learn how to calculate the area of composite figures by breaking them down into simpler shapes.
- Memorize the value of π and understand its significance in calculating the area of circles.
- Work on real-world problems that involve finding the area of various objects or spaces.

Understanding the concept of area and how to calculate it is essential for solving geometry problems and for practical applications in fields such as construction, architecture, and engineering.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

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.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

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

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.