Question

quiz: quiz unit 3 - logic and geometry find the area of the given geometric figure. the area of the figure is (simplify your answer.) (diagram dimensions: 10 m, 17 m, 21 m, 8 m)

Explanation:

Step1: Split the figure into two rectangles

We can split the L - shaped figure into two rectangles. The first rectangle has dimensions \(10\) m (width) and \(17\) m (height). The second rectangle has a width of \(21 - 10=11\) m and a height of \(8\) m.

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 length and \(w\) is width). For the first rectangle, \(l = 17\) m and \(w = 10\) m. So the area \(A_1=10\times17 = 170\) square meters.

Step3: Calculate the area of the second rectangle

For the second rectangle, the length \(l = 8\) m and the width \(w=21 - 10 = 11\) m. Using the area formula for a rectangle, \(A_2=11\times8=88\) square meters.

Step4: Calculate the total area

The total area of the figure is the sum of the areas of the two rectangles. So \(A = A_1+A_2=170 + 88=258\) square meters.

Answer:

\(258\) square meters