First, divide the figure into two shapes so we can calculate each shape’s area easier and add their areas together to get the total area squared. We will construct a line segment continuing from the 5cm segment. This segment also divides the 15cm length into 8cm.
When we construct this segment, we obtain a parallelogram quadrilateral, assuming that all four angles are 90° each. Because we have two pairs of congruent and assumed parallel segments with all four interior angles being 90,° we have a rectangle by definition. Therefore, we can use the area for a rectangle.
Area of rectangle: A=L•W where A is area, L is length, and W is width.
Let’s input the values into the formula:
A=10•8cm^2
*Note that ^2 means square centimeters or centimeters squared.
A=80cm^2
So, we have found the area for the first figure. Now, we need to add this area to the area of the second figure.
We are missing some measurements for the top figure, so let’s use our bottom figure to find its measurements.
Because the base segment of the entire shape is 10cm and the dividing segment we created is 5cm, we know that the top segment of the top figure is 5cm. Because we know the left whole segment is 15cm and the right segment of the bottom figure is 8cm, we can subtract the whole segment by 8 because 8+L=15 where L is the length of the top segment. So, L=15-8 which means L=7. We know have the dimensions for the top figure to calculate its area. This top figure also forms a rectangle.
A=L•W
A=7•5cm^2
A=35cm^2
Now that we have the area of both shapes, we can calculate the total area by adding the two areas together:
80+35=115
So, the area is 115cm^2.