Answer:
Using properties of parallelogram and angle sum property of a triangle in the figure as shown below in the attachment
In parallelogram ABCD, AC is a diagonal.
Given: and
As, we know that opposite angles in parallelogram are equal.
therefore,
Now, in ΔADC
Sum of the measures of angles in a triangle is 180 degree.
Substituting the values of and
we have;
or
Subtract from both sides we get
Therefore, the measure of angle CAD is .
(answer in big text in the end :D )
1. Calculate the SA of all the sides...
There are 5 sides in this shape. 2 sides are Triangles, and 3 are rectangles. Let's call the rectangle on the base, base rectangle, let's call the large rectangle on the right, right rectangle, and the left on on the side, left rectangle. Just so that we can identify them...
Now, first, we will calculate the Triangular parts' surface area. There is a tip in this, as we know, to calculate the area of 1 triangle, we have to use this formula... BUT! that's only for calculating 1 triangle, not 2, but we have 2 here, to use this shortcut, we will just do BxH not 1/2xBxH
Let's do it!
Base of triangle: 9.8ft
Height of triangle: 5.33ft
Now, we have to multiply these
9.8x5.33=52.234
Rounding to the nearest tenth... 52.2
Then, let's do the base rectangle
Length of rectangle: 9.8ft
Width of rectangle: 3.8ft
Now, multiply!
9.8x3.8=37.24
Rounding to the nearest tenth... 37.2
Now, let's do the Right Rectangle
Dimensions:
Length of rectangle: 8.5ft
Width of rectangle: 3.8ft
multiply...
8.5x3.8=32.3
no rounding in this, it's already rounded to the nearest tenth
Now, let's do the left rectangle...
Dimensions:
Length of rectangle: 6.2ft
Width of rectangle: 3.8ft
6.2x3.8=23.56
Rounded to nearest tenth... 23.6
2. Now that we have gotten the SA's of all of the shapes in this triangular prism, let's ADD them together to get our FINAL answer.
All the answers are: 52.2, 37.2, 32.3, and 23.6
<h2>adding them, our answer is: 145.3ft²</h2>