We want to find the area and the perimeter of the given quadrilateral. In order to do so, we first need to examine the given figure to find out the length of the unknown side.
Since a negative side length does not make sense, we only need to consider positive solutions.
Perimeter
Now that we have found out the hypotenuse of the right triangle, we can place its length in the given quadrilateral.
The perimeter of a figure is the sum of the side lengths.
P=8+4+10+10 = 32
Therefore, the quadrilateral's perimeter is 32 units.
Area
Here we will calculate the areas of the rectangle and the right triangle separately. The total area is the sum of both parts.
Let's begin by calculating the area of the triangle.
A=1/2bh
Now we substitute the value of the base, b= 6, and the value of the height, h= 8, into the formula to calculate A.
The area of the triangle is 24 square units. Now, let's calculate the area of the rectangle.
A=l w
Now we substitute the length, l= 4, and the width, w= 8, of the rectangle into the formula to calculate A.
The area of the rectangle is 32 square units. Recall that the total area is the sum of the areas of the right triangle and the rectangle.
A_T = 24 + 32 = 56
Therefore, the total area of the figure is 56 square units.
