Are there no ways of solving
Instead of unfolding it
Because i dnt get the unfolding part

<h2>Surface Area of Prisms and Cylinders</h2>
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<h3>Definition: Surface area</h3>
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<p>Surface area is the total area of the exposed or outer surfaces of a prism.</p>
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<p>This is easier to understand if we imagine the prism to be a cardboard box that we can unfold. A solid that is unfolded like this is called a net. When a prism is unfolded into a net, we can clearly see each of its faces. In order to calculate the surface area of the prism, we can then simply calculate the area of each face, and add them all together.</p>
<p>For example, when a triangular prism is unfolded into a net, we can see that it has two faces that are triangles and three faces that are rectangles. To calculate the surface area of the prism, we find the area of each triangle and each rectangle, and add them together.</p>
<p>In the case of a cylinder the top and bottom faces are circles and the curved surface flattens into a rectangle with a length that is equal to the circumference of the circular base. To calculate the surface area we therefore find the area of the two circles and the rectangle and add them together.</p>
<p>Below are examples of right prisms and a cylinder that have been unfolded into nets:</p>
<h3><strong>Rectangular Prism</strong></h3>
<p><img alt="5f1f23505e095d6d8ee25fefccc03aeb.png" src="https://data.ulearngo.com/assets/004e8333-08a5-4300-a885-776faf18300d"/></p>
<p><img alt="0e9abb941c948ab43f9d07890c2b9428.png" src="https://data.ulearngo.com/assets/e42a5b77-cfc6-4200-8f6e-c72dadcc3e39"/></p>
<p><img alt="bb375ceffeda2562134a69536f40fa5f.png" src="https://data.ulearngo.com/assets/50ed70ff-8d8b-4235-b8cb-6adbe849a845"/></p>
<p>Rectangular prism</p>
<p>A rectangular prism unfolded into a net is made up of six rectangles.</p>
<h3><strong>Cube</strong></h3>
<p><img alt="62baec7eae7924a0c233a4cc273e2696.png" src="https://data.ulearngo.com/assets/15c35118-83f1-4b4e-8eba-81b96ee2a9c7"/></p>
<p><img alt="52ebaf59f995e05925917d6dac6526a0.png" src="https://data.ulearngo.com/assets/cf8e9081-d9a2-42ca-add2-ee22de2b4fda"/></p>
<p><img alt="1bddf1110a311ba257ab0b9b95f1b370.png" src="https://data.ulearngo.com/assets/98d62704-ef79-4c81-ac8b-2366c4c96fe8"/></p>
<p>Cube</p>
<p>A cube unfolded into a net is made up of six identical squares.</p>
<p><strong>Triangular prism</strong></p>
<p><img alt="5aa931be519312ff3aa4c928654bc31c.png" src="https://data.ulearngo.com/assets/b84bdac0-3ab1-4822-a4e9-f5983911d421"/></p>
<p><img alt="4af611bb8f86289851d50d143ae7ebb3.png" src="https://data.ulearngo.com/assets/658a4793-c74e-4527-906e-4b391201f967"/></p>
<p><img alt="c77b31f1c53e40aa7d44ec56407783d4.png" src="https://data.ulearngo.com/assets/d336a0ba-e28d-4914-87c2-6775232a8475"/></p>
<p>Triangular prism</p>
<p>A triangular prism unfolded into a net is made up of two triangles and three rectangles. The sum of the lengths of the rectangles is equal to the perimeter of the triangles.</p>
<p><strong>Cylinder</strong></p>
<p><img alt="59b6e2c3d07b14243c762ebc3ccf7ce9.png" src="https://data.ulearngo.com/assets/777c0abd-04a2-4116-ae2f-528886c838cd"/></p>
<p><img alt="d029260684e1faab093d3a761e05b2da.png" src="https://data.ulearngo.com/assets/4daeaf79-b5f8-41a8-9025-06fcf879b7e6"/></p>
<p>Cylinder</p>
<p>A cylinder unfolded into a net is made up of two identical circles and a rectangle with a length equal to the circumference of the circles.</p>
<div class="note visit">
<p>This video explains how we can unfold solids into nets.</p>
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="360" src="https://www.youtube.com/embed/kqqmJiJez6o?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="640"></iframe></div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<h3>Question</h3>
<div>
<p>Find the surface area of the following rectangular prism:</p>
<img alt="feae5c060473a0bda20bac750c5379eb.png" src="https://data.ulearngo.com/assets/827a071b-1bcf-42bc-990f-3644f7a228d7"/></div>
<div>
<h3>Sketch and label the net of the prism</h3>
<img alt="a0470f2aa9e1c3794573888daf776deb.png" src="https://data.ulearngo.com/assets/59da8e77-367f-4bc4-a9da-ff24ac157b53"/></div>
<div>
<h3>Find the areas of the different shapes in the net</h3>

\begin{align*} \text{large rectangle}&amp; =\text{perimeter of small rectangle}\times \text{length} \\ &amp; = (2 + 5 + 2 + 5)\times 10 \\ &amp; = 14\times 10 \\ &amp; = \text{140}\text{ cm$^{2}$} \\ \\ 2\times \text{small rectangle}&amp; = 2(5\times 2) \\ &amp; = 2(10) \\ &amp; = \text{20}\text{ cm$^{2}$} \end{align*}</div>
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<h3>Find the sum of the areas of the faces</h3>
<p>$\text{large rectangle} + 2\times \text{small rectangle} = 140 + 20 = 160$</p>
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<div>
<h3>Write the final answer</h3>
<p>The surface area of the rectangular prism is $\text{160}$ $\text{cm$^{2}$}$.</p>
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</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<h3>Question</h3>
<div>
<p>Find the surface area of the following triangular prism:</p>
<img alt="d2d6406d9b8adb92d433f8a926c3788c.png" src="https://data.ulearngo.com/assets/9a1fa87c-1005-466e-b77e-5c65c89c7956"/></div>
<div>
<h3>Sketch and label the net of the prism</h3>
<img alt="a7aeaffca0bbc91ff938f90f312fb8e5.png" src="https://data.ulearngo.com/assets/a173daa9-bfa4-47f8-a965-b3a8b9bcb2cc"/></div>
<div>
<h3>Find the area of the different shapes in the net</h3>
<p>To find the area of the rectangle, we need to calculate its length, which is equal to the perimeter of the triangles.</p>
<p>To find the perimeter of the triangle, we have to first find the length of its sides using the theorem of Pythagoras:</p>
<img alt="38a60096eb94af75ed559102d11e0f97.png" src="https://data.ulearngo.com/assets/604832e1-607e-4975-a73d-cd11da7e3e6f"/></div>
<div>
<h3>Find the sum of the areas of the faces</h3>

\begin{align*} \text{surface area}&amp; = \text{area large rectangle} + (2\times \text{area of triangle}) \\ &amp; = 216 + 2(12) \\ &amp; = \text{240}\text{ cm$^{2}$} \end{align*}</div>
<div>
<h3>Write the final answer</h3>
<p>The surface area of the triangular prism is $\text{240}$ $\text{cm$^{2}$}$.</p>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<h3>Question</h3>
<div>
<p>Find the surface area of the following cylinder (correct to 1 decimal place):</p>
<img alt="5ca2d3534241cbcc0b84b4ba9e4ec89c.png" src="https://data.ulearngo.com/assets/fd112f53-71b1-40e1-806c-e8aae7355b68"/></div>
<div>
<h3>Sketch and label the net of the cylinder</h3>
<img alt="c7485581c393b4bc08f1e91205d9e1c1.png" src="https://data.ulearngo.com/assets/c03f438d-e42e-490c-bfb9-ca783c62155c"/></div>
<div>
<h3>Find the area of the different shapes in the net</h3>

\begin{align*} \text{area of large rectangle} &amp; = \text{circumference of circle}\times \text{length} \\ &amp; = 2 \pi r \times l \\ &amp; = 2 \pi (10)\times 30 \\ &amp; = \text{1 884.9555...}\text{ cm$^{2}$} \\ \text{area of circle} &amp; = \pi {r}^{2} \\ &amp; = \pi {(10)}^{2} \\ &amp; = \text{314.1592...}\text{ cm$^{2}$} \end{align*}\begin{align*} \text{surface area}&amp; =\text{area large rectangle}+(2\times \text{area of circle}) \\ &amp; =\text{1 884.9555...} + 2(\text{314.1592...}) \\ &amp; = \text{2 513.3}\text{ cm$^{2}$} \end{align*}</div>
<div>
<h3>Write the final answer</h3>
<p>The surface area of the cylinder is $\text{2 513.3}$ $\text{cm$^{2}$}$.</p>
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Surface Area of Prisms and Cylinders

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Surface Area of Prisms and Cylinders

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