What is the area of the quadrilateral? height is 6cm width is 10cm on the bottom and 6cm on the top
To find the area of the quadrilateral, we first need to find the lengths of the two slant sides. Let's call them a and b.
Using the Pythagorean theorem, we can calculate the lengths of a and b:
a^2 = 10^2 + 6^2
a^2 = 100 + 36
a^2 = 136
a ≈ 11.66 cm
b^2 = 6^2 + 6^2
b^2 = 36 + 36
b^2 = 72
b ≈ 8.49 cm
Now that we have the lengths of all sides, we can calculate the area of the quadrilateral using the formula for the area of a trapezoid:
Area = (1/2) * (top base + bottom base) * height
Area = (1/2) * (6 + 10) * 6
Area = (1/2) * 16 * 6
Area = 48 cm^2
Therefore, the area of the quadrilateral is 48 square centimeters.