Question

What is the area of this trapezoid?

Answer 1

Answer:

$\boxed{Area \: of \: trapezoid = 126 \: {in}^{2}}$

Given:

AB = 12 in.

DF = 2 in.

FE = 12 in.

EC = 2 in.

BE = 9 in.

Step-by-step explanation:

$Area \: of \: trapezoid = \frac{1}{2} (sum \: of \: parallel \: sides) \times height$

Parallel sides are:

AB = 12 in

DC = DF + FE + EC

= 2 + 12 + 2

= 16 in.

Height:

BE = 9 in.

$Area \: of \: trapezoid = \frac{1}{2}(12 + 16) \times 9 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2 } \times 28 \times 9 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 14 \times 9 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 126 \: {in}^{2}$

Answer 2

Answer:

126 in²

Step-by-step explanation:

We can see that this trapezium is made of 2 shapes that we are familiar with which a square and 2 triangles. In order to work out the area of this trapezium we are going to work out the area of each shape and then add it up but first we need to know the formula's so,

→ Area of a triangle = 0.5 × Base × Height

→ Area of a square  = Length × Width

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⇒ First we are going to work out the area of triangle DFA so we utilise the triangle formula

→ Area of a triangle = 0.5 × Base × Height

⇒ Substitute in the values

→ Area of a triangle = 0.5 × 2 × 9

⇒ Simplify

→ Area of a triangle = 9 in²

The area of triangle DFA is 9 in²

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⇒ Next we are going to work out the area of square AFEB so we utilise the square formula

→ Area of a square  = Length × Width

⇒ Substitute in the values

→ Area of a square  = 12 × 9

⇒ Simplify

→ Area of a triangle = 108 in²

The area of square AFEB  is 108 in²

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⇒ Finally we are going to work out the area of triangle ECB so we utilise the triangle formula

→ Area of a triangle = 0.5 × Base × Height

⇒ Substitute in the values

→ Area of a triangle = 0.5 × 2 × 9

⇒ Simplify

→ Area of a triangle = 9 in²

The area of triangle ECB is 9 in²

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Now we add all the area's together so,

9 + 108 + 9 = 126 in²

The area of the trapezium is 126 in²