Question

1. determine the perimeter and area of the figures below.

a)
b)

Explanation:

Step1: Calculate perimeter of figure a

Perimeter of rectangle part + arc length.
$P_a=(10 + 6)\times2-6+\frac{1}{4}\times2\pi\times6$
$=32 - 6+3\pi$
$=26 + 3\pi\approx26+3\times3.14=35.42$ m

Step2: Calculate area of figure a

Area of rectangle + area of quarter - circle.
$A_a=10\times6+\frac{1}{4}\times\pi\times6^{2}$
$=60 + 9\pi$
$=60+9\times3.14 = 88.26$ m²

Step3: Calculate perimeter of figure b

Sum of all side - lengths.
$P_b=(8 + 1.5)\times2+6\times2$
$=19+12=31$ km

Step4: Calculate area of figure b

Area of large rectangle - area of small rectangle.
$A_b=8\times(6 + 1.5)-6\times(8 - 2)$
$=8\times7.5-6\times6$
$=60 - 36=24$ km²

Answer:

a) Perimeter: $26 + 3\pi\approx35.42$ m, Area: $60 + 9\pi\approx88.26$ m²
b) Perimeter: 31 km, Area: 24 km²