Answer:
(x+3)^2+(y+2)^2=80
Step-by-step explanation:
The enclosed shape is that of a trapezoid. The area of a trapezoid is the product of the height of it (measured perpendicular to the parallel bases) and the average length of the two parallel bases. The formula is generally written ...
... A = (1/2)(b₁ + b₂)·h
Here, the base lengths are the y-coordinates at x=4 and x=9. The height is the distance between those two x-coordinates: 9 - 4 = 5.
You are expected to find the y-values at those two points, then use the formula for the area of the trapezoid.
You can save a little work if you realize that the average of the two base lengths is the y-coordinate corresponding to the average x-coordinate: (9+4)/2 = 6.5. That is you only need to find the y-coordinate for x=6.5 and do the area math as though you had a rectangle of that height and width 5.
Going that route, we have
... y = 2(6.5) - 1 = 13 - 1 = 12
Then the trapezoid's area is
... A = 12·5 = 60 . . . . square units.
M= y1-y2/x1-x2
m= 8/10
m= 4/5
Answer:
V = 17.25m cubed
Step-by-step explanation:
Break up the shape into a rectangular prism and a triangular prism. First, find the volume of the rectangular prism. This volume is calculated by the formula b*w*h which would be (2.5)(3)(1.4) which gives the answer 10.5m cubed. Then, find the volume of the triangular prism. The triangular prism can be divided into two triangular prisms so that multiplying b*h of one of them will give the area for the face of both of them (since the formula for the area of the face of a triangle is 1/2b*h) which is necessary for calculation since the formula formula for finding the volume of a triangular prism is A*h. Finding the area of the entire face by multiplying 1.25 and 1.8 will give the answer 2.25m squared. Even though the height for the calculation of the area is 1.8, it's not the height for the calculation of the volume because the height must be found with the triangular face being on the bottom of the prism. Therefore, in order to find the volume, you would do (2.25)(3) in order to get 6.75m cubed. All that is left is to add the 10.5m and 6.75m to get the final answer of 17.25m cubed.
