Question

find the area of the following shapes. Show the formula used and all work. Round to 1 decimal place .

Answer 1

Answer:

$\text{d. }106,250\:\mathrm{cm^2},\\\text{e. }38.5\:\mathrm{cm^2},\\\text{a. }85\:\mathrm{ft^2},\\\text{b. }7.89676\:\mathrm{m^2}$

Step-by-step explanation:

Part D:

The figure shows a parallelogram with base 425 cm and height 250 cm. Its area can be found by $A=bh$ and therefore the area of this shape is $A=425\cdot 250=\boxed{106,250\:\mathrm{cm^2}}$

Part E:

The figure shows a trapezoid. The area of a trapezoid is equal to the average of its bases multiplied by the height. Since one base is 2 cm and the other base is 9 cm, the average of these bases is $\frac{2+9}{2}=\frac{11}{2}=5.5\:\mathrm{cm}$. The height is given as 7 cm, therefore the area of the trapezoid is $7\cdot 5.5=\boxed{38.5\:\mathrm{cm^2}}$

Part A:

The composite figure consists of two rectangles. The area of a rectangle with base $b$ and height $h$ is given by $A=bh$. The total area of the figure is equal to the sum of the areas of these two rectangles.

Area of first rectangle (rectangle on bottom): $5\cdot 13=65\:\mathrm{ft^2}$

Area of second rectangle (rectangle on top):

*Since we don't know the dimensions, we must find them. Start by converting 108 inches to feet:

$108\:\mathrm{in}=9\:\mathrm{ft}$. Therefore, the dimensions of this rectangle are (10-5) ft by (13-9) ft $\implies5\text{ by } 4$ and this rectangle's area is $5\cdot 4=20\:\mathrm{ft^2}$

Thus, the area of the figure is equal to $65+20=\boxed{85\:\mathrm{ft^2}}$

Part B:

We've already found the area of the figure in the previous part in square feet. To find the area in square meters, use the conversion $1\text{ square foot}=0.092903\text{ square meter}$.

Therefore, the area of the figure, in square meters, is $85\cdot 0.092903=\boxed{7.89676\:\mathrm{m^2}}$