---
title: "Composing Shapes"
description: "Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape"
canonical: https://lightmysky.com/learn/mathematics/composing-shapes-mt_MqqR7VUoz1
source: https://lightmysky.com/learn/mathematics/composing-shapes-mt_MqqR7VUoz1.md
retrieved: 2026-10-19
---

> **Agent view.** This is the Markdown twin of the page, for tools and assistants.
> When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md
> API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md
> Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt
> Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json
> Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`.

# Composing Shapes

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape

Subject: Mathematics · Area: Geometry · Ages 6 to 7
Page: https://lightmysky.com/learn/mathematics/composing-shapes-mt_MqqR7VUoz1

## Ready when they can

- Combine two triangles to form a rectangle or larger triangle
- Put together half-circles and quarter-circles to form circles or new shapes
- Decompose a composite shape and describe which simpler shapes make it up
- Names triangles, circles, rectangles, squares and trapezoids by their straight side counts.

## Lesson: Building New Shapes from Shapes

You already know how to put two shapes together to make a new one. Now you will go further. You can put together shapes like triangles, half-circles, and quarter-circles to build new shapes. You can even use the new shape you just built to build something even bigger. Four same-size quarter-circles fit together to make one whole circle, just as two half-circles do.

*(drawing: Two same-size half-circles fit together, flat edge to flat edge, with no gaps. Together they make one whole circle.)*

**Example.** Leo has two same-size triangles, each with one square corner like the corner of a book. He flips one over so their long slanted sides touch with no gaps. Now the two triangles together make one rectangle.

A shape you build, like Leo's rectangle, is called a composite shape. You can use a composite shape like any other piece. Put a triangle on top of the rectangle, and you have built a house. That rectangle uses 2 triangles. Triangles have 3 straight sides. Trapezoids and rectangles have 4. Circles have none.

**Tip.** When you see a shape, look for the smaller shapes inside it: which flat shapes made this one?

**Recap.** Put simple shapes together to build new shapes, then use those new shapes to build something even bigger.

## Practice

16 questions on this page, each with its working shown.

## Needs first

- [2-D shapes](https://lightmysky.com/learn/mathematics/2-d-shapes-mt_KJeEeTutJI)
- [Combining Simple Shapes](https://lightmysky.com/learn/mathematics/combining-simple-shapes-mt_XjwUlmxdCT)

## Opens up

- [Area by Tiling](https://lightmysky.com/learn/mathematics/area-by-tiling-mt_Jvvh5P06NV)