<a href="https://www.math-aids.com/" target="_blank"><b>Math-Aids.Com.</b></a> &nbsp;<b>All rights reserved.</b> <div style="height:100px"></div> </td> <td class="copy" align="right"> <a target="_blank" href="https://www.math-aids.com/Geometry/Volume/">Geometry - Volume Worksheets</a></td> </tr> </table> </td></tr></table> </td></tr></table> <script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)})(window,document,'script','//www.google-analytics.com/analytics.js','ga');ga('create','UA-11626077-1','auto');ga('require','displayfeatures');ga('send','pageview'); <script type="text/javascript"> Show
Here we will learn about the surface area of a triangular prism and how to calculate it. There are also volume and surface area of a triangular prism worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. What is the surface area of a triangular prism?The surface area of a triangular prism is the total area of all of the faces. To work out the surface area of a triangular prism, we need to work out the area of each face and add them all together. Lateral faces are all of the faces of an object excluding the top and the base. For a triangular prism the top and the base are triangles and the lateral faces are rectangular sides. The lateral surface area of a triangular prism is the total area of the rectangular sides The triangular faces of a triangular prism are congruent (exactly the same) but, unless the triangle is isosceles or equilateral, the rectangles are all different. E.g. Since it is an area, surface area is measured in square units (e.g. mm^2, cm^2, m^2 etc). What is the surface area of a triangular prism?How to calculate the surface area of a triangular prismIn order to work out the surface area of a triangular prism:
How to calculate the surface area of a triangular prismSurface area of a triangular prism worksheetGet your free Surface area of a triangular prism worksheet of 20+ questions and answers. Includes reasoning and applied questions. COMING SOON Surface area of a triangular prism worksheetGet your free Surface area of a triangular prism worksheet of 20+ questions and answers. Includes reasoning and applied questions. COMING SOON Surface area of a triangular prism examplesExample 1: finding the surface area of a triangular prism with a right triangleWork out the surface area of the triangular prism
The area of the triangle at the front is \frac{1}{2}\times12\times5 = 30cm^{2} The back face is the same as the front face so the area of the back is also 30cm^{2} . The area of the base is 9\times12=108cm^{2} The area of the left side is 9\times5=45cm^{2} The area of the top is 9\times13=117cm^{2} It will make our working clearer if we use a table:
2Add the five areas together. Total surface area: 30 + 30 + 108 + 45 + 117 = 330 3Include the units. The measurements on the triangular prism are in cm therefore the total surface area of the triangular prism = 330cm^{2} . Example 2: surface area of a triangular prism with an isosceles triangleWork out the surface area of the triangular prism Work out the area of each face.
Add the five areas together. Total surface area: 28.5 + 28.5 + 84 + 140 + 140 = 421 The measurements on the triangular prism are in mm therefore the total surface area of the triangular prism = 421mm^{2} . Example 3: surface area of a right triangular prismThis prism has a triangular base and rectangular sides. We are told the height of the prism is 9cm . We can work out the surface area in exactly the same way, we just adjust the labels we give to each face in our table. Work out the area of each face.
Add the five areas together. Total surface area: 24 + 24 + 90 + 54 + 72 = 264 The measurements on the triangular prism are in cm therefore the total surface area of the triangular prism = 264cm^{2} . Example 4: surface area of a triangular prismWork out the surface area of the triangular prism Work out the area of each face.
Add the five areas together. Total surface area: 210 + 210 + 1400 + 480 + 1480 = 3780 The measurements on the triangular prism are in m therefore the total surface area of the triangular prism = 3780m^{2} . Example 5: surface area of a triangular prism with different unitsWork out the surface area of the triangular prism. Give your answer in mm^{2} . Work out the area of each face. Some of the measurements here are in cm and some are in mm. Since we have been asked for the answer in mm^{2} , we need to convert all measurements to mm : 1.4cm = 14mm and 2.5cm=25mm .
Add the five areas together. Total surface area: 56 + 56 + 200 + 350 + 402.5 = 1064.5 The measurements we have used are in mm therefore the total surface area of the triangular prism = 1064.5mm^{2} . Example 6: surface area when there is a missing lengthWork out the surface area of the triangular prism. Give your answer in cm^{2} . Work out the area of each face. When calculating the surface area we need the length of each side of the triangle. We are told the base and height of the triangle and the length of the prism but we don’t have the length of the hypotenuse of the triangle. To work this out we can use the Pythagorean Theorem a^{2}+b^{2}=c^{2} . \[ 8^{2}+15^{2} = c^{2} \\ 289 = c^{2} \\ \sqrt{289} = c \\ 17 = c \]
Add the five areas together. Total surface area: 60 + 60 + 72 + 135 + 153 = 480 The measurements we have used are in cm therefore the total surface area of the triangular prism = 480cm^{2} . Common misconceptions
Volume and surface area are different things – volume tells us the space within the shape whereas surface area is the total area of the faces. To find surface area, work out the area of each face and add them together.
Usually all of the rectangle have different areas (unless the triangle is isosceles or equilateral).
In surface area questions, we need to know all three side lengths of the triangle however we only need the base and the height to calculate the area of the triangle Surface area of a triangular prism is part of our series of lessons to support revision on triangular prism. You may find it helpful to start with the main triangular prism lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Practice surface area of a triangular prism questionsWork out the surface area of each face:
Work out the surface area of each face:
Work out the surface area of each face:
Work out the surface area of each face:
Notice that some of the measurements are in m and some are in cm . Since we are asked to give the answer in square centimetres, we need to convert all the measurements to cm . 0.5m = 50cm and 0.8m=80cm . Next, Work out the surface area of each face:
In this question, we are missing the height of the triangle. Since it is a right angled triangle, we can use Pythagoras’ theorem to work out the height: \begin{aligned} a^{2}+b^{2}&=c^{2}\\ h^{2}+12^{2}&=13^{2}\\ h^{2}+144&=169\\ h^{2}&=169-144\\ h^{2}&=25\\ h&=5 \mathrm{m} \end{aligned} Next, work out the surface area of each face:
Surface area of a triangular prism GCSE questions1. Work out the surface area of the triangular prism. (3 marks) Show answer \frac{1}{2} \times 0.3 \times 0.4 = 0.06 (1) 1 \times 0.3=0.1, ~1 \times 0.4 – 0.4,~ 1 \times 0.5 = 0.5 (1) 0.06+0.06+0.3+0.3+0.5=1.32 \mathrm{m}^{2} (1) 2. A packaging company wants to minimise the amount of packaging they use. Which of these shapes should they choose to make their packaging? Show how you decide.
(5 marks) Show answer (1) (1) (1) (1) (1) 3. A packaging box is made in the following shape
(5 marks) Show answer (1) (1) (1) (1) (1) Learning checklistYou have now learned how to:
Still stuck?Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. Find out more about our GCSE maths revision programme. How do you find the surface area for a triangular prism?The formula that is used to calculate the surface area of a triangular prism is, Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 ...
What is the formula for triangular surface area?So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle. Example: Find the area of the triangle. The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.
What is the correct formula for a triangular prism?Triangular prism formulas
volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length. area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.
How do you work out the surface area of a prism?The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
|