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Area, Surface Area, and Volume Facts & Worksheets

In this lesson, we will understand how we can find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.

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Area, Surface Area, and Volume Worksheets
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In this lesson, we will understand how we can find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.

See the fact file below for more information on the Area, Surface Area, and Volume or alternatively, you can download our 35-page Area, Surface Area, and Volume worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

AREA OF A RIGHT TRIANGLE

  • In this section, we will solve for the area of a right triangle.
  • As a refresher, remember that in order to find the area of a rectangle, we multiply its width by its length.
    • w x l = a
  • Given this, we can therefore conclude that in order to find the area of a right triangle, we can just use the same formula we use to solve to the area of a rectangle but with an additional operation, which is to divide it by 2. We divide it by 2 since we have already established that a rectangle is composed of two right triangles. Thus, if we solve for the area of a rectangle, we can just divide the area by 2 to find the the area of the right triangle.
  • Therefore, we can write the equation as:
    • area of right triangle = (l x w)/2

AREA OF TRIANGLES

  • Now that we know how to compute for the area of a right triangle, we can derive the equation that we can use to compute for the area of other triangles.
  • Note that any two triangles will form a parallelogram.
  • And we know that to solve for an area of any parallelogram, we just multiply its base and its height.
  • Therefore, we can write the formula for the area of any triangle as:
    • area of triangle = (b x h)/2

AREA OF SPECIAL QUADRILATERALS

  • In this section, we will learn how to solve for the area of special quadrilaterals.
  • We will take a trapezoid as our special quadrilateral example.
  • In this case, we would not be able to use the same equation that we used in parallelograms since this is not a parallelogram.
  • However, we can transform this to create a parallelogram.
  • First, we can duplicate this trapezoid.
  • Now that we have two trapezoids, we have to flip the other one vertically and connect them in order to have a parallelogram.
  • After connecting them both, we have a parallelogram.
  • Remember that for us to be able to find the area of a parallelogram, we have to know its height and base.
  • For us to identify the height and the base, we have to first label them.
  • Based on the diagram above, the height of the parallelogram is already given, however, for the base, we still have to compute for it.
    • base = a + b
  • Now that we know the values of the height and base of the parallelogram we have created, we can now substitute them to the equation we used before.
    • area = base x height
    • area = (a + b) x height
  • But we have to remember that the area that we are computing with the equation above is the area of the parallelogram that we have created using two trapezoids.
  • Therefore, we have to divide it by 2 to acquire the area of just one trapezoid.
    • area = ((a + b) x height)/2
  • Thus, we can compute for the area of a trapezoid using the above equation.
  • We can also use this equation to solve for other equilaterals, we just have to create a parallelogram to apply this.

SURFACE AREA OF A CUBE

  • If area is the measurement of the size of a flat surface in a two-dimensional plane, then surface area is the is the measurement of the exposed surface of a shade in a three-dimensional plane.
  • Let us start with the most simple three-dimensional shape – a cube.
  • We know that to find the area of a square, we just need to multiply one side with another side.
  • On the other hand, a cube has 6 faces and each face can be represented by a square.
  • Therefore, if we want to get the surface area of a cube, we can first get the area of one face (one square).
    • a = s x s
  • But we also have to keep in mind that there are 6 faces in a cube, therefore we have to multiply it by 6.
  • Thus, if we want to get the surface area of a cube, we need to use the equation:
  • surface area = 6 x ( s x s)
    • Wherein s represents the length of the side.

SURFACE AREA OF A RECTANGULAR PRISM

  • To find the area of a rectangle, we just need to multiply the length and the width.
  • Now, a rectangular prism is composed of 6 faces. However, we cannot use the same method we used for computing for the surface area of a cube since the faces of a rectangular prism are not equal.
  • However, we know that the top and the bottom faces are the same, the left and the right faces are also the same, and the front and back faces are also the same.
  • Therefore, we only need to identify 3 rectangular faces.
  • Now, we have to identify 3 face combinations: (1) top and bottom, (2) front and back, and (3) right and left.
  • Let us first identify the top and bottom face combination, to get the area of it, the sides that we have to multiply are side a and side c.
    • top/bottom = a x c
  • Next, we have to identify the area of the front and back face combination. This time, the sides we have to multiply are sides b and c.
    • front/back = b x c
  • Lastly, the right and left faces are to computed by multiplying sides a and b.
    • right/left = a x b
  • Remember that we identified 3 faces, but there are 6 faces in a rectangle. We also identified that the top and bottom are the same, front and back are also the same, and the right and left faces are also the same.
  • Therefore, we need to multiply each equation we got above by 2.
  • After that, we just need to add them all to get the surface area of a rectangular prism.
    • surface area = 2(a x b) + 2(b x c) + 2(a x c)

SURFACE AREA OF A PYRAMID

  • Now, we will try to get the surface area of pyramid.
  • If the triangular faces of a rectangular pyramid are the same, then we can just use the formula for getting the area of a triangle.
  • With that, we can compute for the area of a pyramid by first computing for the perimeter of the base.
  • Since the base is a square, we just need to multiply the length of the side or edge by 4.
    • perimeter = 4s
  • Once we have the value of the perimeter of the base, we need to find the area of the base. From the previous discussions, we know that to get the area of a square, we just need to multiply the length of its side by itself.
    • base area = s x s
  • Now that we have the formulas for the perimeter and the area of the base, we need to remember that to find the area of a triangle we need to follow the formula:
    • area of triangle = (b x h)/2
  • Which is base times height then we divide the value by 2. However, for the surface area of a pyramid we have to alter this a bit.
  • Instead of base, we will replace it with perimeter of the base, and instead of height, we will clearly define it as slant height or length.
  • After that, we will add the area of the base. Therefore, the formula for the surface area of a regular pyramid is:
    • SA of a pyramid = ((p x h)/2) + ba

SURFACE AREA OF ANY PRISM

  • To find the area of any prism, there are just 3 things that we have to remember: (1) base perimeter, (2) base area, and (3) height of the prism.
    • surface area = (p x h) + 2b
  • wherein p stands for the perimeter of the base, h for the height of the prism, and b for the area of the base.

VOLUME OF A CUBE

  • Now that we know how to get the area of a square, and the surface area of a cube, we will now move on to finding the volume of a cube.
  • But first, let us identify what a volume is. Volume is the measurement of how much space a three-dimensional shape occupies.
  • We computed for the area of a square by multiplying its side by itself. Then, we multiplied this by 6 to compute for the surface area of a cube.
  • This time, to find the volume of the cube, we will need to follow this formula:
    • volume = s x s x s
  • where “s” stands for the length of the side.

VOLUME OF A RECTANGULAR PRISM

  • Moving forward, let us not compute for the volume of a rectangular prism.
  • Since we were able to compute for the volume of a cube by multiplying the side to itself twice, we just need to apply this concept to find the volume of a rectangular prism.
  • Therefore, to find the volume of a rectangular prism we just need to follow the formula:
    • volume = l x w x h
  • Where “l” is the length of the prism, “w” is the width of the prism, and “h” is the height of the prism.

VOLUME OF A PYRAMID

  • Where “l” is the length of the prism, “w” is the width of the prism, and “h” is the height of the prism.
  • If for the area of a triangle we used base times height then divide it by 2. This time, for the volume of a pyramid, we will use:
    • volume of a pyramid = (b x h)/3

Area, Surface Area, and Volume Worksheets

This is a fantastic bundle which includes everything you need to know about the Area, Surface Area, and Volume across 35 in-depth pages. These are ready-to-use Area, Surface Area, and Volume worksheets that are perfect for teaching students how we can find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.

Complete List Of Included Worksheets

  • Lesson Plan
  • Area, Surface Area, and Volume
  • Find A
  • D&C
  • Cubes
  • Pyramid
  • Prisms
  • Words
  • VC
  • Find
  • Blank
  • Versus

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Use With Any Curriculum

These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.

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