Respuesta :

Answer :

  • Area(r) = 108 in^2
  • Area(t) = 24 in^2
  • Area(f) = 132 in^2

Explanation :

Area of rectangle is given by,

  • Area(r) = breadth x height
  • Area(r) = 12in x 9in
  • Area(r) = 108 in^2

Area of triangle is given by,

  • Area(t) = 1/2bh
  • Area(t) = 1/2*12in*4in
  • Area(t) = 24 in^2

Area of the figure is given by,

  • Area(f) = Area(r) + Area(t)
  • Area(f) = 108 in^2 + 24 in^2
  • Area(f) = 132 in^2

msm555

Answer:

[tex]\textsf{Area of } \boxed{\quad} = \boxed{\quad 108 \quad } \sf in^2 [/tex]

[tex]\textsf{Area of } \triangle = \boxed{\quad 24 \quad } \sf in^2 [/tex]

[tex]\textsf{Area of Figure } = \boxed{\quad 132 \quad } \sf in^2 [/tex]

Step-by-step explanation:

To find the total area of the figure comprising a rectangle and a triangle, we need to calculate the areas of each shape separately and then add them together.

Given:

Rectangle:

  • Base (b) = 12 in
  • Height (h) = 9 in

Triangle:

  • Base (b) = 12 in
  • Height (h) = 4 in

Area of Rectangle:

[tex] \textsf{Area} = b \times h \\\\ = 12 \times 9 \\\\ = 108 \textsf{in} ^2 [/tex]

Area of Triangle:

[tex] \textsf{Area} = \dfrac{1}{2} \times b \times h \\\\ = \dfrac{1}{2} \times 12 \times 4 \\\\ = 24 \textsf{in}^2 [/tex]

Total Area of Figure:

[tex] \textsf{Total Area} = \textsf{Area of Rectangle} + \textsf{Area of Triangle} \\\\ = 108 + 24 \\\\ = 132 \textsf{in} ^2[/tex]

So, the total area of the figure (rectangle and triangle combined) is 132 in².