Illustrative Math Alignment: Grade 6 Unit 1

Reasoning to Find Area

Lesson 9: Formula for the Area of a Triangle

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Math Example: Comparing Area: Example 5	Math Example: Comparing Area: Example 5 Topic Geometry Description This example compares the areas of two triangles, A and B, nested within a grid. Triangle A has a base of 4 units and a height of 5 units, while Triangle B has a base of 3 units and a height of 5 units. Using the formula for the area of a triangle (1/2 * base * height), we calculate that Triangle A has an area of 1/2 * 4 * 5 = 10 square units, and Triangle B has an area of 1/2 * 3 * 5 = 7.5 square units. Comparing these results, we can conclude that A > B, meaning Triangle A has a larger area than Triangle B.	Area and Perimeter of Quadrilaterals, Area and Perimeter of Triangles and Area and Circumference
Math Example: Comparing Area: Example 6	Math Example: Comparing Area: Example 6 Topic Geometry Description This example compares the areas of a circle (Figure A) and a square (Figure B) drawn on a grid. The circle has a radius of 2 units, while the square has a side length of 4 units. Using the formula for the area of a circle (π r2) and a square (s2), we calculate that the circle has an area of π * 22 = 4π square units, and the square has an area of 42 = 16 square units. Comparing these results, we can conclude that A < B, meaning the square has a larger area than the circle.	Area and Perimeter of Quadrilaterals, Area and Perimeter of Triangles and Area and Circumference
Math Example: Comparing Area: Example 7	Math Example: Comparing Area: Example 7 Topic Geometry Description This example compares the areas of a circle (Figure A) and a triangle (Figure B) drawn on a grid. The circle has a radius of 2.5 units, while the triangle has a base of 4 units and a height of 7 units. Using the formula for the area of a circle (π r2) and a triangle (1/2 * base * height), we calculate that the circle has an area of π * 2.52 = 6.25π square units, and the triangle has an area of 1/2 * 4 * 7 = 14 square units. Comparing these results, we can conclude that A > B, meaning the circle has a larger area than the triangle.	Area and Perimeter of Quadrilaterals, Area and Perimeter of Triangles and Area and Circumference
Math Example: Comparing Area: Example 8	Math Example: Comparing Area: Example 8 Topic Geometry Description This example compares the areas of two complex shapes (Figures A and B) made up of rectangles, displayed on a grid. Both figures have identical areas calculated as 3 * 6 - 1 - 1 = 16 square units. By comparing these results, we can conclude that A = B, meaning both shapes have equal areas despite their different appearances.	Area and Perimeter of Quadrilaterals, Area and Perimeter of Triangles and Area and Circumference
Math Example: Comparing Area: Example 9	Math Example: Comparing Area: Example 9 Topic Geometry Description This example compares the areas of two complex shapes (Figures A and B) drawn on a grid. Figure A is a shape with multiple right angles, while Figure B is similar but slightly smaller. Calculating their areas, we find that Figure A has an area of 4 * 7 - 2 - 2 = 24 square units, and Figure B has an area of 4 * 7 - 3 - 3 = 22 square units. Comparing these results, we can conclude that A > B, meaning Figure A has a larger area than Figure B.	Area and Perimeter of Quadrilaterals, Area and Perimeter of Triangles and Area and Circumference
MATH EXAMPLES--Teacher's Guide: Triangle Area and Perimeter	MATH EXAMPLES--Teacher's Guide: Triangle Area and Perimeter This set of tutorials provides 40 examples of how to find the area and perimeter of triangles. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Area and Perimeter of Triangles
MATH EXAMPLES--Triangle Area and Perimeter	MATH EXAMPLES--Triangle Area and Perimeter This set of tutorials provides 40 examples of how to find the area and perimeter of triangles. NOTE: The download is a PPT file.	Area and Perimeter of Triangles
Video Tutorial: Perimeter of a Triangle	Video Tutorial: Perimeter of a Triangle In this video tutorial learn about perimeter in the context of triangles. Several examples of calculating a perimeter are shown: whole number sides, decimal sides. Then we look at triangles one of whose sides is a variable. The resulting perimeter is an algebraic expression. Finally, explore a situation where the perimeter is known but one of the side lengths is a variable. This results in an equation that can be solved for the variable.	Area and Perimeter of Triangles