Answer:
Step-by-step explanation:
Part 1). In a pentagon when attach the center to all vertices, five triangles are formed with the given height h = 8 inches and base b = 10 inches.
Now area of the pentagon = 5(Area of one triangle formed by center and two vertices of the pentagon)
= 5([tex]\frac{1}{2})(Base)(height)[/tex]
= [tex]\frac{5}{2}(b)(h)[/tex]
= 2.5×10×8
= 200 inch²
Part 2). Area of parallelogram = [tex]\frac{1}{2}(\text{Sum of two parallel sides})(\text{Distance between the parallel sides})[/tex]
Area = [tex]\frac{1}{2}(6+6)(5)[/tex]
= [tex]\frac{60}{2}=30[/tex] cm²
Composite area of the figure = Area of a triangle + Area of the rectangle
Area of the triangle = [tex]\frac{1}{2}(Base)(height)[/tex]
= [tex]\frac{1}{2}(4-2)(9-5)[/tex]
= [tex]\frac{1}{2}(2)(4)[/tex]
= 4 m²
Area of rectangle = Length×width = 2×9 = 18m²
Area of the composite figure = 4 + 18 = 22 m²
Part 3). a.Coordinates of point x will be [tex][\frac{1}{2}(x_{1}+x_{2}), \frac{1}{2}(y_{1}+y_{2})][/tex]
= [tex][\frac{1}{2}(0+2b), \frac{1}{2}(0+2c)][/tex]
= (b, c)
b. Coordinates of Y will be = [tex][\frac{1}{2}(x_{1}+x_{2}), \frac{1}{2}(y_{1}+y_{2})][/tex]
= [tex][\frac{1}{2}(2a+2b), \frac{1}{2}(0+2c)][/tex]
= [(a + b), c]
c. Slope of XY = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{c-c}{a+b-b}[/tex]
= 0
d. Slope of PR = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{0-0}{2a-0}=0[/tex]
