Question

from unit 1, lesson 15
find the surface area of this triangular prism.
all measurements are in meters.

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A = \frac{1}{2}bh$. For the triangular faces with base $b = 0.6$ and height $h=0.8$, $A_{triangle}=\frac{1}{2}\times0.6\times0.8 = 0.24$. Since there are 2 triangular faces, the total area of triangular faces is $2\times0.24 = 0.48$.

Step2: Calculate area of first rectangular face

The first rectangular face has dimensions $1\times1.2$, so its area $A_{rect1}=1\times1.2 = 1.2$.

Step3: Calculate area of second rectangular face

The second rectangular face has dimensions $1\times1.2$, so its area $A_{rect2}=1\times1.2 = 1.2$.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions $0.6\times1.2$, so its area $A_{rect3}=0.6\times1.2 = 0.72$.

Step5: Calculate total surface - area

The total surface area $A$ of the triangular prism is the sum of the areas of the triangular and rectangular faces. $A=0.48 + 1.2+1.2 + 0.72=3.6$.

Answer:

$3.6$