Question

find the area of the figure pictured below.
3 m
10 m
4 m
11 m
area = \boxed{} m²
question 11
find the surface area and volume of the sphere.

Explanation:

Step1: Divide the figure into two rectangles

We can split the L - shaped figure into two rectangles. One rectangle has dimensions \(3\space m\times10\space m\) and the other has dimensions \((11 - 3)\space m\times4\space m\) (since the total length is \(11\space m\) and we already have a \(3\space m\) segment in the first rectangle).

Step2: Calculate the area of the first rectangle

The area of a rectangle is given by the formula \(A = l\times w\), where \(l\) is the length and \(w\) is the width. For the first rectangle with \(l = 10\space m\) and \(w=3\space m\), the area \(A_1=10\times3 = 30\space m^{2}\).

Step3: Calculate the area of the second rectangle

The length of the second rectangle is \(11 - 3=8\space m\) and the width is \(4\space m\). Using the area formula for a rectangle, \(A_2 = 8\times4=32\space m^{2}\).

Step4: Calculate the total area

The total area of the figure is the sum of the areas of the two rectangles. So, \(A = A_1+A_2=30 + 32=62\space m^{2}\).

Answer:

\(62\)