4. for each diagram, draw a net with the dimensions labelled and use it to calculate the surface area of the 3 - d shape.
a.
b.
c.

Question

Accepted Answer

# Explanation:
## Step1: Identify the 3 - D shapes
a is a rectangular prism, b is a right - triangular prism, c is a right - triangular prism.
## Step2: Draw the net for the rectangular prism (a)
The net of a rectangular prism has 6 rectangles. Two rectangles with dimensions 6 cm×8 cm, two with 6 cm×10 cm and two with 8 cm×10 cm.
## Step3: Calculate the surface area of the rectangular prism (a)
The surface area formula for a rectangular prism $SA = 2(lw+lh + wh)$, where $l = 10$ cm, $w = 8$ cm, $h = 6$ cm.
$$
\begin{align*}
SA&=2((10\times8)+(10\times6)+(8\times6))\
&=2(80 + 60+48)\
&=2\times188\
&=376\text{ cm}^2
\end{align*}
$$
## Step4: Draw the net for the first right - triangular prism (b)
The net has two right - angled triangles with legs 3 m and 4 m and three rectangles with dimensions: one $3\times5$ m, one $4\times5$ m and one $5\times8$ m.
## Step5: Calculate the surface area of the first right - triangular prism (b)
The area of each right - angled triangle $A_{triangle}=\frac{1}{2}\times3\times4 = 6\text{ m}^2$.
The areas of the rectangles are $A_1=3\times5 = 15\text{ m}^2$, $A_2=4\times5=20\text{ m}^2$, $A_3 = 5\times8=40\text{ m}^2$.
$$
\begin{align*}
SA&=2\times6+15 + 20+40\
&=12+15 + 20+40\
&=87\text{ m}^2
\end{align*}
$$
## Step6: Draw the net for the second right - triangular prism (c)
The net has two right - angled triangles with legs 7 cm and 12 cm and three rectangles with dimensions: one $7\times20$ cm, one $12\times20$ cm and one $13\times20$ cm (using Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $c=\sqrt{7^{2}+12^{2}}=\sqrt{49 + 144}=\sqrt{193}\approx13$ cm).
The area of each right - angled triangle $A_{triangle}=\frac{1}{2}\times7\times12=42\text{ cm}^2$.
The areas of the rectangles are $A_1 = 7\times20=140\text{ cm}^2$, $A_2=12\times20 = 240\text{ cm}^2$, $A_3=13\times20=260\text{ cm}^2$.
$$
\begin{align*}
SA&=2\times42+140+240 + 260\
&=84+140+240+260\
&=724\text{ cm}^2
\end{align*}
$$

# Answer:
a. Surface area of the rectangular prism is $376\text{ cm}^2$
b. Surface area of the right - triangular prism is $87\text{ m}^2$
c. Surface area of the right - triangular prism is $724\text{ cm}^2$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the 3 - D shapes

Step2: Draw the net for the rectangular prism (a)

Step3: Calculate the surface area of the rectangular prism (a)

Step4: Draw the net for the first right - triangular prism (b)

Step5: Calculate the surface area of the first right - triangular prism (b)

Step6: Draw the net for the second right - triangular prism (c)

Answer: