EngageNY
An Area Formula for Triangles
Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....
Shodor Education Foundation
Triangle Area
While the lesson focuses on right triangles, this activity offers a great way to practice the area of all triangles through an interactive webpage. The activity begins with the class taking a square paper and cutting in in half; can they...
EngageNY
Perimeter and Area of Triangles in the Cartesian Plane
Pupils figure out how to be resourceful when tasked with finding the area of a triangle knowing nothing but its endpoints. Beginning by exploring and decomposing a triangle, learners find the perimeter and area of a triangle. They...
Curated OER
Areas of Geometric Shapes with the Same Perimeter
A triangle, square, hexagon, and circle all have a perimeter of one unit. Eighth graders must attempt to find the area of each and arrange them in order from least to greatest areas. A terrific task for applying four different...
Government of Hong Kong
Areas and Volumes - 2D Shapes
Unfortunately for young mathematicians, the world isn't made entirely of parallelograms, triangles, and trapezoids. After first learning the area formulas for these common shapes, students apply this new knowledge to...
Willow Tree
Area of Common Geometric Figures
Scholars can use area formulas, but can they apply what they know about area? The activity challenges learners to think logically while practicing finding area of shapes such as rectangles, circles, parallelograms, triangles, and other...
Curated OER
Developing Formulas for Triangles and Quadrilaterals
In this geometry worksheet, 10th graders determine the area of triangles, parallelograms, trapezoids, kites, and rhombuses. The one page worksheet contains eleven problems. Answers are included.
Alabama Learning Exchange
What You Know About the Bermuda Triangle?
Get lost in the classifications. Using the backdrop of the Bermuda Triangle, pupils classify it by angle and side measures. They also learn information about the triangle and its history.
Alabama Learning Exchange
Triangle Area: No Height? Use the Sine
No height? No problem! Learners use their knowledge and a little help from GeoGebra to develop the Law of Sines formula. The Law of Sines helps to determine the height of triangles to calculate the area.
Illustrative Mathematics
Same Base and Height, Variation 2
This is a good model for learners to visualize triangles of the same base and height. They can can begin to comprehend that these triangles will have the same area no matter how the triangle is drawn. It is part of a series of resources...
Illustrative Mathematics
Area of a Trapezoid
Here is a straightforward example of how to apply the Pythagorean Theorem to find an unknown side-length of a trapezoid. Commentary gives additional information on proving that the inside of the trapezoid is a rectangle, but is...
Curated OER
Area Formulas
Teach your pupils to calculate the area of different polygons. Learners create formulas to solve their problems. They use the TI navigator to graph their shapes and observe the change in area.
EngageNY
Using Trigonometry to Determine Area
What do you do when you don't think you have enough information? You look for another way to do the problem! Pupils combine what they know about finding the area of a triangle and trigonometry to determine triangle area when they don't...
EngageNY
Real-World Area Problems
Not all structures take the shape of a polygon. The 21st lesson in a series of 29 shows young mathematicians they can create polygons out of composite shapes. Once they deconstruct the structures, they find the area of the composite figure.
Curated OER
Triangles
This unit enables scholars to apply the rule for area of a triangle (area equals half base times height). They practice multiplication and division strategies as they calculate areas.
EngageNY
Perimeter and Area of Polygonal Regions in the Cartesian Plane
How many sides does that polygon have? Building directly from lesson number eight in this series, learners now find the area and perimeter of any polygon on the coordinate plane. They decompose the polygons into triangles and use Green's...
EngageNY
Composite Area Problems
The 21st segment in a 28-part series provides learners with area problems involving composite figures. To find the solution, pupils must decide whether to add or subtract areas. The composite figures are composed of quadrilaterals,...
Illustrative Mathematics
Finding Areas of Polygons, Variation 1
An exercise in finding the area of polygons by decomposing into triangles and composing into rectangles is the focus of this resource. Make several copies of the worksheet for each participant. Ask learners to use colored pencils to...
Alabama Learning Exchange
Polygons-Changing Area Versus Changing Perimeter
Investigate the area and perimeter of polygons in this geometry lesson. Young geometers use grid paper to draw a quadrilateral and calculate its area and perimeter. They also read The Greedy Triangle to identify the changing shape of...
EngageNY
Properties of Area
What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.
Curated OER
Finding the Area of an Equilateral Triangle
The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...
Curated OER
Area of Tangram Pieces
Mathematicians calculate the area of a tangram piece without using formulas. They use a geometry journal to record activities during this lesson. They make a set of tangrams and use them to compute area. They use...
Curated OER
Finding the Area of Shapes
In this area of shapes unit, upper graders participate in hands-on problem solving activities to find the formulas for the area of a parallelogram, a triangle, and a trapezoid. They manipulate the geoboard to explore relationships among...
Hotchalk
Triangle Sum Theorem
Your visual geometry learners will appreciate triangle drawings as they model the triangle sum theorem and algebraically solve to find the missing interior angle in a triangle. Practice problems increase in complexity and vary in their...