Question

He figure shows a parallelogram inside a rectangle outline:

A parallelogram is shown within a rectangle. The length of the rectangle is 3 over 5 foot, and the width of the rectangle is 2 over 5 foot. The two equal bases of the triangles outside the parallelogram are labeled 1 over 5 foot.

What is the area of the parallelogram?
1 over 25 square foot
11 over 25 square foot
3 over 25 square foot
4 over 25 square foot

Answer 1

4/25 foot²

Explanation:

Refer to attachment*

Answer 2

Consider the attachment first for a better understanding, now after considering the attachment you will gotta know that, the height of the parallelogram is just same as the width of the rectangle i.e (2/5) foot and but for the base of the parallelogram we can subtract the base of one triangle from the length of the rectangle, so it will give us (3/5) - (1/25) = (2/5), so now we have breadth as well as height of the parallelogram, so now, as area of a parallelogram is given by it's height times it's base, so we will be having

`{:\implies \quad \sf Area_((Parallelogram))=(2)/(5)* \frac25}`

`{:\implies \quad \boxed{\bf{Area_((Parallelogram))=(4)/(25)\:\: sq.\:\:foot}}}`

Hence, Option D) is correct

Well, we have another method for it, we can subtract the area of both the triangles from the area of rectangle, and now,as their base of the triangle is (1/5) foot and height is same as the width of rectangle i.e (2/5) foots, so its area will be (1/2) times base times height, but as here are two triangles, so multiplying the area of one triangle by 2 will vanish 2, so now we just have

`{:\implies \quad \sf Area_((Parallelogram))=\bigg((2)/(5)* (3)/(5)\bigg)-\bigg((1)/(5)* (2)/(5)\bigg)}`

`{:\implies \quad \sf Area_((Parallelogram))=(6)/(25)-(2)/(25)}`

`{:\implies \quad \boxed{\bf{Area_((Parallelogram))=(4)/(25)\:\: sq.\:\:foot}}}`

This also, proves that the correct answer is D)