Find the area of the figure. Round to the nearest tenth if necessary.
T(-1,8), U(3,5), V(4,0), R(-3,0), S(-3,5)
did you plot the points ???
https://www.wolframalpha.com/input/?i=plot+(-1,8),+(3,5),+(4,0),+(-3,0),+(-3,5),+(-1,8)
looks like by joining (-3,5) and (3,5), I now have a trapezoid, (easy to figure out)
and a triangel with a horizontal base and countable height.
let me know what you get
To find the area of the figure, we need to determine the shape of the figure first. In this case, the given coordinates T, U, V, R, and S suggest that it is a polygon.
To calculate the area of a polygon, we can use various methods, such as dividing it into triangles and then summing up their areas. In this case, the figure appears to be a trapezoid formed by connecting the points T, U, V, R, and S.
To calculate the area of the trapezoid, we can use the formula:
Area = (base₁ + base₂) × height / 2
The bases of the trapezoid can be determined by finding the lengths of the sides TU and VR, while the height can be determined by finding the distance between the base TU and the parallel base VR.
Using the distance formula to find the lengths of the bases and the height:
Length of TU = √((x₂ - x₁)² + (y₂ - y₁)²)
Length of VR = √((x₂ - x₁)² + (y₂ - y₁)²)
Height = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the coordinates of the points:
Length of TU = √((3 - (-1))² + (5 - 8)²)
Length of VR = √((4 - (-3))² + (0 - 0)²)
Height = √((4 - (-1))² + (0 - 5)²)
Simplifying the calculations:
Length of TU = √(4² + (-3)²) = √(16 + 9) = √25 = 5
Length of VR = √(7² + 0²) = √(49 + 0) = √49 = 7
Height = √(5² + (-5)²) = √(25 + 25) = √50 = 5√2
Now we have all the values needed to calculate the area:
Area = (5 + 7) × (5√2) / 2
= 12 × (5√2) / 2
= 6 × (5√2)
= 30√2
Rounding the answer to the nearest tenth, the area of the figure is approximately 42.4 square units.
To find the area of the figure, we can use the formula for the area of a quadrilateral:
Area = 1/2 * |x1y2 + x2y3 + x3y4 + x4y1 - y1x2 - y2x3 - y3x4 - y4x1|
First, let's label the coordinates:
T(-1,8), U(3,5), V(4,0), R(-3,0), S(-3,5)
Next, we can plug in the coordinates into the formula:
Area = 1/2 * |(-1*5) + (3*0) + (4*0) + (-3*8) - (8*0) - (5*4) - (0*-3) - (0*(-1))|
Simplifying the equation:
Area = 1/2 * |-5 + 0 + 0 - (-24) - 0 - 20 - 0 - 0|
Area = 1/2 * |-5 + 24 - 20|
Area = 1/2 * |-1|
Area = 1/2
Therefore, the area of the figure is 0.5 square units.