Question

1. a = ________ p = ________

Explanation:

Step1: Calculate area of rectangle

The rectangle has length $l = 20$m and width $w = 10$m. Area of rectangle $A_{rect}=l\times w=20\times10 = 200$m².

Step2: Calculate area of semi - circle

The semi - circle has diameter $d = 10$m, so radius $r=\frac{d}{2}=5$m. Area of semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi\times5^{2}=12.5\pi$m².

Step3: Calculate area of trapezoid

The trapezoid has bases $b_1 = 20$m, $b_2 = 10$m and height $h = 10$m. Area of trapezoid $A_{trapezoid}=\frac{(b_1 + b_2)h}{2}=\frac{(20 + 10)\times10}{2}=150$m².

Step4: Calculate total area

$A=A_{rect}+A_{semicircle}+A_{trapezoid}=200 + 12.5\pi+150=350 + 12.5\pi$m².

Step5: Calculate perimeter

For the perimeter, we consider the outer - side lengths. The lengths of the rectangle part contribute $20+10$m, the curved part of the semi - circle has length $\frac{1}{2}\times2\pi r=\pi\times5 = 5\pi$m, and the non - parallel sides of the trapezoid and the bottom base of the trapezoid contribute $10\sqrt{2}+10$m (using Pythagorean theorem for non - parallel sides of trapezoid with height 10m and base difference 10m).
$P=20 + 10+5\pi+10\sqrt{2}+10=40 + 5\pi+10\sqrt{2}$m.

Answer:

$A = 350+12.5\pi$m², $P=40 + 5\pi+10\sqrt{2}$m