Question

11
abcd - трапеция
s_abcd - ?
b 8 c
a 16 40 8 16 d

Explanation:

Step1: Recall trapezoid - area formula

The area formula of a trapezoid is $S=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height.

Step2: Identify parallel - sides and height

The lengths of the parallel sides are $a = 8$ and $b=16 + 40+8 + 16=80$, and the height $h$ can be found from the right - angled triangles formed. Since the non - parallel sides are equal (as indicated by the marks), we can consider the symmetry of the trapezoid. The height $h$ can be calculated using the Pythagorean theorem in one of the right - angled triangles. However, we can also use the fact that we can split the trapezoid into a rectangle and two congruent right - angled triangles. The height of the trapezoid is the same as the height of the right - angled triangle. If we consider the base of the right - angled triangle formed on the side, we can find that the height $h = 8$.

Step3: Calculate the area

Substitute $a = 8$, $b = 80$ and $h = 8$ into the area formula $S=\frac{(8 + 80)\times8}{2}$. First, calculate the sum of the parallel sides: $8+80 = 88$. Then, multiply by the height and divide by 2: $S=\frac{88\times8}{2}=88\times4 = 352$.

Answer:

352