Base Times Height: Area of Triangles and Parallelograms

About This Resource

A complete Grade 6 math pack on the area of parallelograms and triangles: why a parallelogram has the same area as a rectangle, why a triangle is half a parallelogram, using the perpendicular height, finding a missing base or height, and composite shapes. Includes a lesson plan, worksheet, quiz, homework, A5 flashcards, a rubric, detailed slides with speaker notes, Word files and answer keys.

Overview

Students discover the area formulas by cutting and rearranging paper shapes. A parallelogram can be cut and moved to make a rectangle, so its area is base × height. Two identical triangles make a parallelogram, so a triangle's area is half of base × height. Students practise choosing the perpendicular height (not the slanted side), find missing measurements, and work out the area of composite shapes such as a house shape.

Resource Details

Subject: Math
Topic: Area of Triangles and Parallelograms
Category: Shapes & Geometry
File Type: PDF
File Size: 311.9 KB
Published: 30 Oct 2026
Downloads: 0

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Grade 6 (ages 11–12) 50 minutes Geometry area formulas multiplication reasoning problem solving

Learning Objectives

Find the area of a parallelogram using A = base × height.
Find the area of a triangle using A = 1/2 × base × height.
Use the perpendicular height, find missing measurements and calculate the area of composite shapes.

How to Use This Resource

Give each student a paper parallelogram to cut and rearrange into a rectangle.
Teach both formulas and the idea of perpendicular height with the slides, then use worksheet activities 1 to 6.
Use the quiz to check learning and send the homework page home.

Classroom Activity Ideas

Cut and rearrange: students cut a triangle off one end of a paper parallelogram and move it to make a rectangle.
Double the triangle: students trace a triangle twice, cut both out and join them to make a parallelogram.
Design a flag: students design a flag made of rectangles and triangles and calculate its total area.

Differentiation

Support: use grid paper and count squares to check each answer. Challenge: find the area of trapezoids by splitting them into a rectangle and triangles.

Assessment

Activities 1 and 2 and the quiz check the formulas; activities 3 to 6 check height, missing measurements and composite shapes. Use the rubric for activity 6.

Teacher Tips

Students often multiply by the slanted side. Draw the height as a dashed line with a small square to show the right angle every time.

What's Included

10-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (6 words with meanings and examples)
Student worksheet (6 activities)
Quiz / assessment (4 parts)
Homework practice page
Printable flashcards: 6 A5 picture cards (separate PDF)
Assessment rubric (4 levels)
Lesson slides (editable PowerPoint)
Editable Word version of all student pages
Complete answer key (also as a separate PDF)