Answer:
A.) SA = 524.48 units squared
B.) SA = 310.93 units squared
C.) SA = 542.36 units squared
Step-by-step explanation:
Note: SA = Surface Area
A.) Area of Triangle (x2) + Area of a Rectangle (x3)
Triangle: -A right triangle
1.) Find The Length, Width, and Height
Length = 16, Width = 9.6, Height = ?
- For this part we will cut the triangle in half
A^2 + B^2 = C^2
A^2 + 8^2 = 9.6^2
A^2 + 64 = 92.16
A^2 = 28.6
A = <em>aprox</em> 5.35
So Height is 5.35
2.) Find Area
A = (1/2)B*H
A = 16*5.35
A = 85.6
We then multiply this by two for the 2nd triangle.
A = 171.2
We then fin the area for the 3 rectangles
A = L*W
Rectangle 1:
A = 12.8*9.2
A = 117.76
Rectangle 2:
A = 9.6*9.2
A = 88.32
Rectangle 3:
A = 16*9.2
A = 147.2
We then sum up all the areas and get
SA = 147.2+88.32+117.76+171.2
SA = 524.48 units squared
B.) Area of a Rectangle (x4) - different sizes + Area of a trapezoid (x2)
1.)Find area of Both Trapezoids, front and back
A = (1/2)(base1+base2)*height
A = (1/2)(9.2+12.5)(6)
A = 21.7*3
A = 65.1
We then multiply it by two for the one at the back and get
A = 130.2
2.) Find Area of Rectangles
Rectangles Left and Right:
A = 5.3*6.2
A = 32.86
Times 2
A = 65.72
Rectangle Top:
A = 12.5*5.3
A = 66.25
Rectangle Bottom:
A = 9.2*5.3
A = 48.76
We then sum up all the areas and get
SA = 48.76+66.25+65.72+130.2
SA = 310.93 units squared
C.) Area of a Rectangle (x4) - different sizes + area of a triangle (x2) and its rectangle (x2)
1.) Find area of front and back
Rectangle:
L = 15.2, H = 4
Triangle:
H = 5 - (get this by subtracting 4 from 9, which is the original height)
B = 15.2
Area of Rectangle + Area of Triangle
A = (15.2*4) + (.5*5*15.2)
A = 60.8 + 38
A = 98.8
We then multiply by 2 for the one at the back and get
A = 197.6
2.) Find Area of Rectangles
Right Rectangle:
A = 4*7.8
A = 31.2
Left Rectangle:
A = 9*7.8
A = 70.2
Top:
A = 16*7.8
A = 124.8
Bottom:
A = 15.2*7.8
A = 118.56
Then we sum up all the areas and get
SA = 118.56+124.8+70.2+31.2+197.6
SA = 542.36 units squared
