Let
be the volume of the solid S. We can write:
![V_{shaded} = V_{triangular} - V_{rectangular}](https://tex.z-dn.net/?f=V_%7Bshaded%7D%20%3D%20V_%7Btriangular%7D%20-%20V_%7Brectangular%7D)
Now, we just need to calculate the volume of the original prism (Vtriangular) and the volume that was removed (Vrectangular). So:
![\bullet ~V_{triangular} = S_{\triangle basis}\times h\\\\ V_{triangular} = \dfrac{5\times5.7}{2}\times4\\\\ V_{triangular} = 57~u^3\\\\\\ \bullet ~V_{rectangular} = S_{\square basis}\times h\\\\ V_{rectangular} = 1.7^2\times4\\\\ V_{rectangular} = 11.56~u^3](https://tex.z-dn.net/?f=%5Cbullet%20~V_%7Btriangular%7D%20%3D%20S_%7B%5Ctriangle%20basis%7D%5Ctimes%20h%5C%5C%5C%5C%0AV_%7Btriangular%7D%20%3D%20%5Cdfrac%7B5%5Ctimes5.7%7D%7B2%7D%5Ctimes4%5C%5C%5C%5C%0AV_%7Btriangular%7D%20%3D%2057~u%5E3%5C%5C%5C%5C%5C%5C%0A%5Cbullet%20~V_%7Brectangular%7D%20%3D%20S_%7B%5Csquare%20basis%7D%5Ctimes%20h%5C%5C%5C%5C%0AV_%7Brectangular%7D%20%3D%201.7%5E2%5Ctimes4%5C%5C%5C%5C%0AV_%7Brectangular%7D%20%3D%2011.56~u%5E3)
Then,
![V_{shaded} = V_{triangular} - V_{rectangular}\\\\ V_{shaded} = 57 - 11.56\\\\ V_{shaded} = 45.44~u^3\\\\ \boxed{V_{shaded} \approx 45.4~u^3}](https://tex.z-dn.net/?f=V_%7Bshaded%7D%20%3D%20V_%7Btriangular%7D%20-%20V_%7Brectangular%7D%5C%5C%5C%5C%0AV_%7Bshaded%7D%20%3D%2057%20-%2011.56%5C%5C%5C%5C%0AV_%7Bshaded%7D%20%3D%2045.44~u%5E3%5C%5C%5C%5C%0A%5Cboxed%7BV_%7Bshaded%7D%20%5Capprox%2045.4~u%5E3%7D)
Thus, the answer is 45.4 u³.
Answer:
larger is 119. smaller is 27
Step-by-step explanation:
x=larger y=smaller
x+y=146
x=5y-16
x=-y+146
5y-16=-y+146
6y=162
y=27
x=119
Based on the calculations, the area of a rectangle to the nearest hundredth is equal to 1143.92 ft².
<h3>How to calculate the area of a triangle?</h3>
Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
<u>Where:</u>
- b represents the base area.
By drawing a line between the points representing wicket 3 and wicket 9, we can logically deduce that wicket 2 forms a perpendicular bisector. Thus, the distance between the points representing wicket 3 and wicket 9 is given by:
Distance = 1/2 × 36.77
Distance = 36.77/2
Distance = 18.39 ft.
For the height of this triangle, we would apply Pythagorean's theorem:
h² = 25.02² - 18.39²
h² = 626.0004 - 338.1921
h² = 287.8083
h = √287.8083
h = 16.97 ft.
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 36.77 × 16.97
Area of triangle = 311.99 ft².
For area of the rectangle, we have:
Mathematically, the area of a rectangle can be calculated by using this formula;
Area = LW
Area = 36.77 × 31.11
Area = 1143.92 ft².
Read more on area of a rectangle here: brainly.com/question/25292087
#SPJ1
the answer is in the attachment
Hope it helps