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This trapezoid has been divided into two right triangles and a rectangle.

How can the area of the trapezoid be determined using the area of each shape?

Enter your answers in the boxes.

The area of the triangle on left is
in², the area of the triangle on the right is
in², and the area of the rectangle is
in².

The area of the trapezoid is the sum of these areas, which is
in².

This trapezoid has been divided into two right triangles and a rectangle How can the area of the trapezoid be determined using the area of each shape Enter your class=

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Answer:

We can determine the sum of the area of the trapezoid if we add up all of the areas of each individual shape.

Step-by-step explanation:

The triangles:

formula= ½ x b x h

½ x 2 x 9

1 x 9 = 9.

We are then going to double this, since these triangles are exactly the same.

So, 18in² is the total area of the triangles.

For the rectangle:

formula= l x w

12 x 9 = 108.

Let’s combine these totals:

108+18 = 126in²

TOTAL AREA = 126in²

Area of a figure divided in pieces is sum of areas of those pieces. The blank options can be filled with values as:

  • The area of the triangle on left is 9 in², the area of the triangle on the right is 9 in²,  and the area of the rectangle is 108 in².
  • The area of the trapezoid is the sum of these areas, which is 126 in².

How to find the area of a region?

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

Base of triangle AFD = b = 2 in.

Height of triangle AFD = h= 9 in.

Thus, area of AFD triangle = [tex]\dfrac{1}{2} \times 2 \times 9 = 9 \: \rm in^2[/tex]

The triangle BEC is of same dimensions as that of the triangle AFD, thus, its area is same, 9 inches squared.

Area of rectangle ABEF = length times width = [tex]12 \time 9 = 108 \: \rm in^2[/tex]

Thus, area of trapezoid ABCD = Area of AFD + Area of BEC + area of ABEF

Area of ABCD = 9 + 9 + 108 square inches = 126 square inches.

Thus, The blank options can be filled with values as:

  • The area of the triangle on left is 9 in², the area of the triangle on the right is 9 in²,  and the area of the rectangle is 108 in².
  • The area of the trapezoid is the sum of these areas, which is 126 in².

Learn more about total area of a region here:

https://brainly.com/question/15096475

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