Find the area of the isosceles trapezoid below by using the area formulas for rectangles and triangles.
a = 6cm b = 9cm and c = 3 cm
To find the area of the isosceles trapezoid, we will first treat it as a rectangle and a triangle.
The formula for the area of a rectangle is:
Area = length * width
Since side a and side b are parallel and equal in length (6cm), we can treat the rectangle as being 6cm in length and 9cm in width.
Area of rectangle = 6cm * 9cm = 54 cm^2
Next, we treat the triangle on top of the rectangle. The base of the triangle is the sum of side b and side c, which is 9cm + 3cm = 12cm. The height of the triangle is equal to side a, which is 6cm.
The formula for the area of a triangle is:
Area = 0.5 * base * height
Substitute the values we have:
Area of triangle = 0.5 * 12cm * 6cm = 36 cm^2
Now we can find the total area of the isosceles trapezoid by adding the area of the rectangle and the area of the triangle:
Total area = Area of rectangle + Area of triangle
Total area = 54 cm^2 + 36 cm^2 = 90 cm^2
Therefore, the area of the isosceles trapezoid with side lengths a = 6cm, b = 9cm, and c = 3cm is 90 square centimeters.