Answer:
The area of the shaded section of the shape is found by calculating the area of the larger trapezoid and subtracting the area of the smaller triangle. The trapezoid's area is 280 cm² and the triangle's area is 44 cm². So, the shaded section has an area of 236 cm².
Step-by-step explanation:
The shaded area is the area of the trapezoid minus the area of the triangle. So, let's find the area of these two shapes.
Trapezoid:
The equation for area of a trapezoid is [tex]A = \frac{b_1+b_2}{2} *h[/tex], where b is the length of the bases and h is the height. Plugging our givens into the equation, we get:
[tex]A_1 = \frac{25+15}{2} *14\\A_1=20*14 = 280[/tex]
So, the area of the trapezoid is 280 cm².
Triangle:
The equation for the area of a triangle is [tex]A = \frac{1}{2} bh[/tex], where b is the length of the base and h is the height. Plugging our givens into the equation, we get:
[tex]A_2 = \frac{1}{2} *11*8=44[/tex]
So, the area of the triangle is 44 cm².
Shaded Area:
Now, to find the area of the shaded section, subtract the area of the triangle from the area of the trapezoid. We get:
[tex]A_s=A_1-A_2\\A_s=280-44=236[/tex]
So, the area of the shaded section is 236 cm².
