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Area, Surface Area, and Volume

  • Grade 6
  • Mathematics
  • 6.G.A.1
  • Geometry
  • ★ Enrichment

Aligned to 6.G.A.1 — Common Core State Standards for Mathematics.

What this lesson teaches

The area of a triangle is half the area of a rectangle with the same base and height, so its formula is one-half base times height. You can also find the volume of a prism and use a net, the unfolded flat version of a solid, to find its surface area.

Worked examples

Example 1

Find the area of a triangle with base 6 and height 4. Multiply base times height (6 times 4 = 24), then take half: 24 divided by 2 is 12.

Example 2

A parallelogram with base 9 and height 5 has area 9 × 5 = 45 — no halving, unlike a triangle.

Example 3

A rectangular prism 3 by 4 by 5 has volume 60 cubic units, but surface area 2(12 + 15 + 20) = 94 square units. One fills, the other wraps.

Practice questions

  1. Find the area of a triangle with base 10 and height 3.
  2. Why is a triangle's area half of a rectangle's?
  3. What is a net of a shape used for?

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Área, Área de Superficie y Volumen

El área de un triángulo es la mitad del área de un rectángulo con la misma base y altura, por lo que su fórmula es la mitad de la base por la altura. También puedes encontrar el volumen de un prisma y usar una red, que es la versión plana y desplegada de un sólido, para calcular su área de superficie.

Ejemplo 1: Encuentra el área de un triángulo con base 6 y altura 4. Multiplica la base por la altura (6 × 4 = 24), luego toma la mitad: 24 ÷ 2 = 12.

Ejemplo 2: Un paralelogramo con base 9 y altura 5 tiene área 9 × 5 = 45 — sin dividir entre dos, a diferencia del triángulo.

Ejemplo 3: Un prisma rectangular de 3 por 4 por 5 tiene volumen 60 unidades cúbicas, pero área superficial 2(12 + 15 + 20) = 94 unidades cuadradas. Uno llena, el otro envuelve.

More Geometry lessons

Volume with Fractional Edges6.G.A.2Polygons on the Coordinate Plane6.G.A.3Nets and Surface Area6.G.A.4

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