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NEED HELP ASAP 50 POINTS!!

Base of the Triangle=__m
Side of the Square =__m
Area of the Triangle = m^2
Area of the Square = m^2
Area of Composite = m^2

NEED HELP ASAP 50 POINTS Base of the Trianglem Side of the Square m Area of the Triangle m2 Area of the Square m2 Area of Composite m2 class=

Respuesta :

roohafzah

Answer :

  • Base of the Triangle= 0.6 m
  • Side of the Square = 0.6 m
  • Area of the Triangle = 0.27 m^2
  • Area of the Square = 0.36 m^2
  • Area of Composite = 0.63 m^2

Explanation :

first,let us find the base of the triangle using the pythagoras theorem,

  • base = √((hypotenuse)^2 - (perpendicular)^2)

here,the triangle is divided in two congruent triangles thus,base would be twice √((hypotenuse)^2 - (perpendicular)^2)

  • base = 2*√((37in)^2 - (35in)^2)
  • base = 2*√144in
  • base = 2*12 in
  • base = 24 in

to convert the units to m,we simply multiply by 0.0254 m

  • 24 in = 24*0.0254 m
  • 24 in = 0.6 m ( 1 d.p. )

______

side of the square = base of the triangle

  • side of the square = 0.6 m ( 1 d.p. )

_______

area of the triangle = 1/2*base*height

to find the area in m^2, we need to convert the height's unit to meters

  • 35in = 35*0.254 m
  • 35in = 0.9 m ( 1 d.p. )

thus,

the area of the triangle would be equal to

  • 1/2*0.6m*0.9m
  • 0.27 m^2

_______

area of a square is equivalent to its side squared

  • area = (0.6m)^2
  • area = 0.36 m^2

_______

thus, area of composite figure would be equal to the area the triangle and that of the square

  • 0.27 m^2 + 0.36 m^2
  • 0.63 m^2
msm555

Answer:

[tex]\sf \textsf{Base of the Triangle}= \boxed{0.60 } m[/tex]

[tex]\sf \textsf{Side of the Square }=\boxed{ 0.60} m[/tex]

[tex]\sf \textsf{Area of the Triangle} = \boxed{0.27 } m^2[/tex]

[tex]\sf \textsf{Area of the Square }= \boxed{0.37 } m^2[/tex]

[tex]\sf \textsf{Area of Composite} =\boxed{0.64 } m^2[/tex]

Step-by-step explanation:

Given:

  • Hypotenuse (h) = 37 inches
  • Height (v) = 35 inches

Convert Hypotenuse and Height to Meters:

[tex] \begin{aligned} h &= 37 \, \textsf{in} \times 0.0254 \, \textsf{m/in} \\ &= 0.9398 \, \textsf{m} \\ v &= 35 \, \textsf{in} \times 0.0254 \, \textsf{m/in} \\ &= 0.889 \, \textsf{m} \end{aligned} [/tex]

Calculate Half Base (Base of the Triangle):

[tex] \begin{aligned} \textsf{Half Base} &= \sqrt{h^2 - v^2} \\&= \sqrt{(0.9398 \, \textsf{m})^2 - (0.889 \, \textsf{m})^2} \\&= \sqrt{0.88322404 \, \textsf{m}^2 - 0.790321 \, \textsf{m}^2} \\&= \sqrt{0.09331904 \, \textsf{m}^2} \\&= 0.3048 \\ & = 0.30 \, \textsf{m (in nearest hundredth)} \end{aligned} [/tex]

Calculate Full Base (Base of the Triangle):

[tex] \begin{aligned} \textsf{Base of the Triangle} &= 2\times \textsf{Half Base} \\ &= 2 \times 0.3048 \, \textsf{m} \\ &= 0.6096\\ & = 0.61 \, \textsf{m (in nearest hundredth)} \end{aligned} [/tex]

Side of the Square (Equal to the Base of the Triangle):

[tex] \textsf{Side of the Square} = \textsf{Base of the Triangle} = 0.6096 \\ = 0.60 \, \textsf{m} \textsf{(in nearest hundredth)}[/tex]

Area of the Triangle:

[tex] \begin{aligned} \textsf{Area of the Triangle} &= \dfrac{1}{2} \times \textsf{Base of the Triangle} \times\textsf{Height} \\&= \dfrac{1}{2} \times 0.6096 \,\textsf{m} \times 0.889 \, \textsf{m} \\&= 0.2709672 \\ & 0.27 \, \textsf{m}^2\textsf{(in nearest hundredth)}\end{aligned} [/tex]

Area of the Square:

[tex] \begin{aligned} \textsf{Area of the Square} &= (\textsf{Side of the Square})^2 \\&= (0.6096 \, \textsf{m})^2 \\&= 0.37161216 \\ & 0.37 \, \textsf{m}^2\textsf{(in nearest hundredth)} \end{aligned} [/tex]

Area of the Composite Figure (Triangle + Square):

[tex] \begin{aligned} \textsf{Area of Composite Figure} &= \textsf{Area of Triangle} + \textsf{Area of Square} \\&= 0.2709672 \, \textsf{m}^2 + 0.37161216 \, \textsf{m}^2 \\&= 0.64257936\\ & = 0.64 \, \textsf{m}^2\textsf{(in nearest hundredth)} \end{aligned} [/tex]

Therefore, the area of the composite figure, converted to meters, is approximately [tex]\boxed{0.64 \, \textsf{m}^2}[/tex].

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