Question

14. Joe just purchased an oddly shaped piece of property, depicted in the figure below. 10 yds 13 yds I 12 yds 15 yds 24 yds What is the area, in square yards, of Joe's new property?​

Answer 1

The Area of Piece of Land is  = 150 +$24\sqrt{11}$  squared yards

What is Area of Trapezium?

The area of a trapezium can be calculated using the lengths of two of its parallel sides and the distance (height) between them.

As the yard is in shape of Trapezium.

We have to find the area of trapezium.

Area of piece of property = Area of Triangle +  Area of rectangle + Area of Triangle

Area of Triangle I,

base = $\sqrt{(13)^{2}{-(12)^{2}}$ = $\sqrt{169-144}$= 5yds

Area = $\frac{1}{2}*b*h$

        =0.5 x 5 x 12

       = 30 squared yds

Area of rectangle = length x breadth

                             = 10 x 12

                             = 120 squared yds

Area if Triangle II, base = $\sqrt{(15)^{2}{-(7)^{2}}$= $\sqrt{225-49}$= $4\sqrt{11}$

Area= $\frac{1}{2}*b*h$

        =0.5 x $4\sqrt{11}$  x 12

        = $24\sqrt{11}$ squared yds

Area of piece of land = 30 + 120 + $24\sqrt{11}$

                                    = 150 +$24\sqrt{11}$ squared yards

Hence, the area of piece of land= 150 +$24\sqrt{11}$  squared yards

Learn more about Area of Trapezium here:

brainly.com/question/16904048

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