Find Area of Triangles and Special Quadrilaterals

Students decompose and rearrange triangles and quadrilaterals to derive area formulas. They apply A = (1/2)bh for triangles and corresponding formulas for parallelograms, trapezoids, and rhombuses, using fractional and decimal dimensions.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 6 · Geometry: Area and Surface Area · question 1 of 3

0 of 20

20 rungs. A star at the top.

Rectangle CDEF is drawn with lengths. Find its area.

Your answer:

How it is taught

0:00 of 4:30

Area of a parallelogram is base times height.

Height is the perpendicular distance, not the slant.

Read it: Area from a rectangle

Triangle ABC has a base of 12 and a dashed height of 5 that meets the base at a right angle. The rectangle around it is 12 × 5 = 60, and the triangle is half of it: 30 square units.

Find the base, and the dashed height at a right angle to it, not a slanted side.
Multiply them: 12 × 5 = 60 is the rectangle around the triangle.
Take half: 60 ÷ 2 = 30.

Two copies of the triangle fit together into the 12 by 5 rectangle, so one triangle is half of it.

A parallelogram becomes a rectangle when the triangle at one end moves to the other end, so its area is base × height.

A trapezoid and a copy of it turned round make a parallelogram, so the trapezoid is half of that parallelogram.

Rectangle and parallelogram: base × height. Triangle: 1/2 × base × height.

Forgetting the half: 12 × 5 = 60 is the rectangle, not the triangle.

The triangle is half the rectangle: 1/2 × 12 × 5 = 30.

A triangle has base 18 and height 9. Its area is ___ square units. — 81. A triangle is half its rectangle: 18 × 9 = 162, and half of that is 81.

Triangle with base 8 and height 5

Here's a triangle. Its base is 8 units and its height is 5 units.

Grade 6 · Using A = ½ × base × height

Here's our triangle — just three sides meeting at three corners.

The base is the bottom side. It's 8 units long.

The height is how tall the triangle stands — measured straight up from the base. It's 5 units.

The area of any triangle equals one-half times the base times the height.

Let's plug in our numbers: one-half times 8 times 5.

First, multiply the base and height: 8 times 5 is 40.

Now take half of 40. Half of 40 is 20.

The triangle's area is 20 square units. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Standard

CCSS.6.G.A.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes

Grade 6

Quoted from the Common Core State Standards.

Where this sits

Comes after

Leads to

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 6

This is one rung of 46 in Grade 6 mathematics, in the order they build on each other.

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free