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The equation can be used to calculate the surface area of the triangular prism.
It is given that the triangular prism net showing in the figure with dimensions.
It is required to find which equation can be used to find the surface area of the triangular prism net.
<h3>What is surface area?</h3>It is defined as the area of 3-dimensional geometry surfaces area sum which is occupying the outer area of the object.
We know the area of a rectangle = length × width
Area of the top rectangle = 13×10
Area of the middle rectangle = 12×10
Area of bottom rectangle= 5×10
The formula for finding the area of a triangle:
Area of right triangle =
Area of left triangle =
The surface area = Area of top+ Area of middle+ Area of bottom+ Area of
a right triangle+ Area of the left triangle
Thus, the equation can be used to calculate the surface area of the triangular prism.
Learn more about the surface area here:
Answer:
<u>The width of the road = 25.359 m</u>
Step-by-step explanation:
See the attached figure which represents the problem.
The length of AB = 40 m
let the width of the road w.
Construct PC perpendicular to AB, So, the measure of angle C = 90°
∠B = 60° and ∠A = 45°
Let the length of AC = x, so, the length of BC = 40-x
At ΔBCP which is a right triangle at C
tan B = opposite/adjacent = w/(40-x)
w = (40-x) * tan B ⇒(1)
At ΔACP which is a right triangle at C
tan A = opposite/adjacent = w/x
w = x * tan A ⇒(2)
from (1) and (2)
(40-x) * tan B = x * tan A
40 tan B - x *tan B = x tan A
40 tan B = x tan A + x *tan B
40 tan B = x (tan A + tan B)
x = (40 tan B)/(tan A + tan B) = (40 tan 60)/(tan 60 + tan 45) = 25.359 m
substitute at (2) with x
w = x tan A = 25.359 tan 45 = 25.359 m
<u>So, The width of the road = 25.359 m</u>
