Surface Area of Shapes 2

Topics

Geometry

Surface Area and Volume

Surface Area of Shapes

Surface Area of Shapes 2

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Question 1 of 7

1. Question

Find the surface area of the figure

Round your answer to two decimal places

`\text(Surface Area )=` (617.92) `\text(cm)^2`

Hint

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Area of a Triangle Formula

`\text(Area )=1/2 times``\text(base)``times``\text(height)`

Area of a Rectangle Formula

`\text(Area )=``\text(length)``times``\text(height)`

Showing and Labelling the Surfaces

We need to add the areas of all the faces of the figure: the two triangles and the three rectangles

First, to find the area of the triangle, get the height that is perpendicular to its base.

Label the sides of the right triangle formed within a triangle

Use the Pythagorean Theorem Formula to solve for `a`, which is equal to the `\text(height)`

`a^2``+``b^2`	`=`	`c^2`	Pythagoras’ Theorem Formula
`\text(h)^2``+``4^2`	`=`	`7^2`	Plug in the known lengths
`\text(h)^2+16`	`=`	`49`	Evaluate `4^2` and `7^2`
`\text(h)^2`	`=`	`33`	Subtract `16` from both sides
`\text(height)`	`=`	`5.74 \text(cm)`	Take the square root of both sides

Next, solve for the area of the triangles using the Area of a Triangle formula

Note that there are two triangles with the same lengths, so we will multiply this area by `2` for the surface area

`\text(Area)`_{`\text(triangles)`}	`=`	`1/2 times``\text(base)``times``\text(height)`

	`=`	`1/2 times``8``times``5.74``=``22.96 \text(cm)^2`

Now, solve for the area of the rectangles using the Area of a Rectangle formula

Note that there are two rectangles with the same lengths, so we will multiply the first area by `2` for the surface area

`\text(Area)`_{`\text(equal rectangles)`}	`=`	`\text(length)``times``\text(height)`
	`=`	`7``times``26``=``182 \text(cm)^2`

`\text(Area)`_{`\text(middle rectangle)`}	`=`	`\text(length)``times``\text(height)`
	`=`	`8``times``26``=``208 \text(cm)^2`

Finally, add all the areas to find the surface area of the figure

`\text(SA)`	`=`	`(2times``22.96``)+(2times``182``)+``208`	Plug in the areas
`\text(SA)`	`=`	`617.92 \text(cm)^2`

The given measurements are in centimetres, so the area is measured as square centimetres

`\text(SA)=617.92 \text(cm)^2`

Question 2 of 7

2. Question

What is the surface area of this Rectangular Prism?

Surface Area`=` (320)`mm^2`

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Incorrect

Surface Area of a Rectangular Prism

`SA= 2 xx (color(royalblue)(text(width)) xx color(green)(text(height)) + color(orange)(text(depth)) xx color(green)(text(height)) + color(royalblue)(text(width)) xx color(orange)(text(depth)))`

Labelling the given lengths

`color(royalblue)(text(width)=12)`

`color(green)(text(height)=7)`

`color(orange)(text(depth)=4)`

Use the formula to find the surface area

`SA`	`=`	`2 xx (color(royalblue)(text(width)) xx color(green)(text(height)) + color(orange)(text(depth)) xx color(green)(text(height)) + color(royalblue)(text(width)) xx color(orange)(text(depth)))`	Surface area of a Rectangular Prism formula

	`=`	`2 xx (color(royalblue)(text(12)) xx color(green)(text(7)) + color(orange)(text(4)) xx color(green)(text(7)) + color(royalblue)(text(12)) xx color(orange)(text(4)))`	Plug in the known lengths

	`=`	`320`	Simplify

	`=`	`320 \ mm^2`

The given measurements are in millimetres, so the surface area is measured as millimetres squared

Volume`=320 \ mm^2`

Question 3 of 7

3. Question

Find the surface area of the Cone

Round your answer to `1` decimal place

Use `pi=3.141592654`

`\text(Surface Area )=` (7710.7, 7706.8, 7713.8) `\text(cm)^2`

Hint

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Correct

Correct!

Incorrect

Surface Area of a Closed Cone

`\text(SA )=pi times``\text(radius)^2` `+pi times``\text(radius)``times``\text(length)`

We need to used the slanted length of the cone