Question

The figure shows a parallelogram inside a rectangle outline: A parallelogram is shown within a rectangle. The length of the rectangle is 1 over 2 foot and the width of the rectangle is 1 over 3 foot. The two equal bases of the triangles outside the parallelogram are labeled 1 over 6 foot. What is the area of the parallelogram? 1 over 9 square foot 1 over 6 square foot 1 over 5 square foot 1 over 3 square foot

Answer 1

To find the area of the parallelogram you will need to find the distance of the base which is part of the length of the rectangle. To find this distance you will subtract 1/2 and 1/6. The height of the parallelogram is the same as the width of the rectangle.

Please see the attached picture for the work and a visual representation.

The answer is 1/9 ft.² .

Answer 2

The area of parallelogram is $\frac{1}{9} foot^{2}$

What is rectangle?

A  plane figure with four straight sides and four right angles, especially one with unequal adjacent sides

What is parallelogram?

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal).

What is area of parallelogram?

Area of quadrilateral is equal to the product of length and height of the parallelogram.

Area of quadrilateral = b × h

where b= breath of  parallelogram

          h= height of  parallelogram ( height is always perpendicular )

A parallelogram is within a rectangle.

Length of rectangle = $\frac{1}{2} foot$

Width of rectangle = $\frac{1}{3}foot$

Side of triangle outside the rectangle = $\frac{1}{6} foot$

now side of parallelogram which lie on rectangle = length of side of rectangle - length of side of triangle

$\frac{1}{2} foot - \frac{1}{6} foot$

= $\frac{2}{6} foot$

$= \frac{1}{3} foot$

now Area of parallelogram = Breath * height

in parallelogram height = breath of rectangle = $\frac{1}{3} foot$

Area of parallelogram = $\frac{1}{3} * \frac{1}{3}$

Area of parallelogram = $\frac{1}{9} foot^{2}$

Hence the Area of parallelogram = $\frac{1}{9} foot^{2}$

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