Question

Using the digits 0-9 at most one time each, fill in the blanks to create a quadrilateral with an area of 16 square units​

Answer 1

To create a quadrilateral with an area of 16 square units, one can use dimensions such as 4 and 4 (for a square) or 2 and 8 (for a rectangle), as these dimensions multiplied together result in 16.

Step-by-step explanation:

The question involves creating a quadrilateral with an area of 16 square units using the digits 0-9 at most one time each. To create a quadrilateral with an area of 16 square units, we need to find two dimensions that when multiplied together equal 16. One possible pair of dimensions is 4 and 4, since 4×4 equals 16. Therefore, for our quadrilateral, we might choose a square with side lengths of 4 units. However, the instructions do not specify the shape of the quadrilateral, so a rectangle with sides of 2 units and 8 units would also work, as 2×8 is 16 as well.

These examples illustrate the relationship between the dimensions of geometric shapes and their areas, which is a crucial concept in geometry. The side length of a larger square being twice that of a smaller square would have an area four times larger, due to the area being proportional to the square of the side length.

Answer 2

Step-by-step explanation:

In order to solve this problem, let's choose a trapezoid which is a quadrilateral where at least one pair of opposite sides are parallel. The area (A) of this shape is given by:

`A=((b_(1)+b_(2))h)/(2) \\ \\ \\ Where: \\ \\ b_(1),b_(2):Are \ parallel \ bases \\ \\ h:height`

Since we must use the digits 0-9 at most one time, let's choose digits 2, 4 and 6 this way:

`b_(1)=2 \\ \\ b_(2)=6 \\ \\ h=4`

Then, the area is:

`A=((2+6)4)/(2) \\ \\ A=(32)/(2) \\ \\ A=16 \ sq \ units`

So our quadrilateral satisfies the given statement.