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1 month ago

Amir is laying stone for his new patio. The diagram of the patio is shown. How many

Mathematics

1 answer:

Leona [12.6K]1 month ago

7 0

Answer: 108ft^2

Step-by-step explanation:

Initially, we observe two right triangles at the top.

The area of a right triangle can be calculated by taking half the product of its perpendicular sides.

A shared perpendicular side for both triangles is known to be 6ft.

Both triangles utilize the same base, which measures 14ft in length; therefore, each triangle's base is half of that, giving us 7ft.

14ft/2 = 7ft

Consequently, each triangle has a side of 6ft and another side of 7ft.

Thus, the area of each right triangle located at the top is:

6ft*7ft/2 = 21ft^2

Having two of such triangles results in an area of:

A1 = 21ft^2 + 21ft^2 = 42ft^2.

Next, examining the lower portion, we can break it down into two right triangles and one rectangle.

The lower side measures 8ft, with the differential from the 14ft side being:

14ft - 8ft = 6ft

(This calculation ensures that the length of the bottom edge matches the top edge for rectangle formation).

This gives a surplus of 6ft that we can split into both right triangles (3ft each, this defines one of the triangles' sides).

Notably, the dimensions of each triangle are 6ft and 3ft for the respective other side,[ [TAG_42]]

leading us to the area calculation:

A = 6ft*3ft/2 = 9ft^2

Thus, for two triangles, A2 totals to 18ft^2.

Moreover, the rectangle involved is 8ft by 6ft, giving an area of:

A3 = 8ft*6ft = 48ft^2

Collectively summing up all found areas yields:

A1 + A2 + A3 = 42ft^2 + 18ft^2 + 48ft^2 = 108ft^2

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1 month ago