Homeschool Math
Homeschool Math: Area of Triangles
This lesson presents the idea that the area of any triangle is exactly half of a certain parallelogram -- thus we get the familiar formula of multiplying the base and the altitude and taking half of that. The lesson contains varied...
Better Lesson
Better Lesson: Finding the Area of a Triangle
Sixth graders find the area of a triangle using square units and the area formula.
Better Lesson
Better Lesson: Area of Composite Shapes
Sixth graders take their knowledge about area of rectangles, squares and triangles and apply it to parallelograms, trapezoids, and composite shapes.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Equal Area Triangles on the Same Base Ii
This task has students apply their knowledge of parallel lines to solve a geometric problem on areas of triangles. The task is open-ended in that students can choose their method of completing the task. Aligns with G-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Srt Finding the Area of an Equilateral Triangle
This task examines how to calculate the area of an equilateral triangle two ways: using triangle congruence and using trigonometric ratios. Aligns with G-CO.C.10 and G-SRT.C.
Better Lesson
Better Lesson: Finding the Area of a Trapezoid
Sixth graders find the area of a trapezoid by decomposing it into triangles and using the formula
Illustrative Mathematics
Illustrative Mathematics: G Gpe Equal Area Triangles on the Same Base I
This task is a relatively easy application of the formula for the area of a triangle and the use of parallel lines. Aligns with G-GPE.B.5.
Illustrative Mathematics
Illustrative Mathematics: 6.g Same Base and Height, Variation 1
Make the following triangles on a geoboard. Remember that the pegs are equally spaced in a square grid. Compare the areas of the triangles. Aligns with 6.G.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Gpe, G Co, G Srt Unit Squares and Triangles
In this task, students are shown three unit squares and two line segments connecting two pairs of vertices. They are asked to find the area of a triangle formed by intersecting lines. They can solve it using coordinate geometry or...
Better Lesson
Better Lesson: Finding the Area Review and Assessment
Sixth graders find the area of rectangles, triangles, parallelograms, and trapezoids by using formulas or by composing into rectangles or triangles.
Illustrative Mathematics
Illustrative Mathematics: 6.g Same Base and Height, Variation 2
This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models. They still determine the area of each...
Homeschool Math
Homeschool Math: Area of Parallelograms
This lesson presents the idea that the area of any right triangle is exactly half of a certain rectangle, and contains varied exercises for pupils.
Science and Mathematics Initiative for Learning Enhancement (SMILE)
Smile: Geometry Distance of Triangles Using a Protractor
Basic exercises are presented to help students understand the concept of the area of triangles and the angles of a triangle.
Illustrative Mathematics
Illustrative Mathematics: G Gpe Triangle Perimeters
Students are shown two triangles touching points on a coordinate grid and are asked to answer questions about their perimeters. The purpose of this task is to apply the Pythagorean theorem to calculate distances and areas. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: 6.g Base and Height
The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs. Aligns with 6.G.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Srt Extensions, Bisections, Dissections in Rectangle
In this task, students must draw a diagram from a verbal description and use their understanding of similar triangles to find the area of a quadrilateral. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G C Mutually Tangent Circles
Three circles are mutually tangent. Students are asked to find the total area of the circles plus the area inside where they meet. Students will need to know how to calculate the area of a circle, a sector of a circle, and an equilateral...
Illustrative Mathematics
Illustrative Mathematics: 8.g Circle Sandwich
Eighth graders are presented with a drawing of a large square inscribed by a circle which is itself inscribed by a second square. They are asked to find the area of the circle outside the smaller square and compare it to the area of the...
Illustrative Mathematics
Illustrative Mathematics: 8.g Two Triangles' Area
In this task, 8th graders are given the dimensions of two isosceles triangles and are asked to compare their areas. They must draw them and use the Pythagorean Theorem and the triangle area formula to solve the problem. Aligns with 8.G.B.7.
Illustrative Mathematics
Illustrative Mathematics: G C, G Srt Setting Up Sprinklers
In this task, students must decide where to place sprinklers on a lawn so that the maximum area of the lawn will be watered. To solve it, they must find areas of sectors of circles and use trigonometric ratios to solve right triangles....
Illustrative Mathematics
Illustrative Mathematics: A sse.b.4: Triangle Series
The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation....
Illustrative Mathematics
Illustrative Mathematics: 6.g Polygons in the Coordinate Plane
The purpose of this task is for students to practice plotting points in the coordinate plane and finding the areas of polygons. This task assumes that students already understand how to find areas of polygons by decomposing them into...
Illustrative Mathematics
Illustrative Mathematics: G C, G Srt Neglecting the Curvature of the Earth
Jerry and Ashley are trying to find out if it is possible to see the lowest point in the USA from the highest point in the USA. It turns out that the highest point in the United States, the peak of Mount Whitney, is only 85 miles from...
OER Commons
Oer Commons: Polygons
Seventh graders find the area of regular polygons, recalling what they already know about the area of geometric shapes and generalizing a formula for any regular polygon.