Virginia SOL Math / Grade 8 / Measurement & Geometry

8.MG.5

Area & Perimeter of Composite Figures

What you'll learn

  • Find the area and perimeter of composite plane figures
  • Break a composite figure into familiar shapes
  • Solve practical problems involving composite figures

Words to know

Composite figure —
a shape made of two or more simpler shapes
Perimeter —
the distance around the outside of a figure
Area —
the number of square units that cover a figure
Decompose —
break a figure into simpler parts
Semicircle —
half of a circle

Why it matters Composite figures model real spaces like L-shaped rooms and running tracks, where we combine simple shapes to find area or perimeter.

Worked examples

Model ItI do

An L-shape is a 10 by 6 rectangle with a 4 by 3 rectangle removed from a corner. Find its area.

Find the full rectangle area: 10 times 6 = 60. Subtract the removed piece: 4 times 3 = 12. The area is 60 - 12 = 48 square units.

Try It TogetherWe do

A figure is a 8 by 5 rectangle with a semicircle of radius 4 on one 8-unit end. Find the area. Use 3.14 for pi.

Rectangle area is 8 times 5 = 40. Semicircle area is half of pi times radius squared = 0.5 times 3.14 times 16 = 25.12. Total area is 40 + 25.12 = 65.12 square units.

Now YouYou do

A shape is a 12 by 4 rectangle joined to a 4 by 4 square. Find the total area.

Find each area and add them. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.A 4 by 4 square and a 4 by 2 rectangle are joined. Find the total area.

  2. 2.Find the area of a 10 by 5 rectangle with a 2 by 2 square removed.

  3. 3.Find the perimeter of a 6 by 3 rectangle.

On Level

The core Quick Check from the book.

  1. 1.A 5 by 5 square and a 5 by 2 rectangle are joined. Find the total area.

  2. 2.Find the area of a 9 by 4 rectangle with a 2 by 2 square removed.

  3. 3.A semicircle has radius 6. Find its area. Use 3.14 for pi.

  4. 4.Two 3 by 3 squares are joined side by side. Find the area.

  5. 5.A rectangle is 7 by 3. A second rectangle 3 by 3 is added on. Find the total area.

Challenge

Stretch your thinking.

  1. 1.A figure is a 12 by 6 rectangle with a semicircle of radius 3 on one 6-unit end. Find the total area. Use 3.14 for pi.

  2. 2.An L-shaped room is a 10 by 8 rectangle with a 4 by 3 rectangle cut from a corner. Find the area.

  3. 3.A shape is a 8 by 5 rectangle with a triangle of base 8 and height 6 on top. Find the total area.