Question

Use the composite figures below to more each statement as true or false.Justify your choices. Please I need it in 40 minutes.A.The area of the figure A can be found by determining the sun of the area of the rectangle and the area of a semicircle.B. the area of figure b can be found by decomposing the figure into a square and parallelogram.C.Figure b has a total area of 29.75 M2.D.the area of figure a is 45.99 m2 more than the area of figure B.

Answer 1

A)

Notice that this figure is composed by a rectangle and two semicircles.

Then, we need to add twice the area of a semicircle and the area of the rectangle to find the total area of the figure.

Therefore, the first statement is false.

B)

Notice that a line can be drawn to figure B so that it is separated into a square and a parallelogram:

Then, statement B is true.

C)

The square hasa side with length 3.5m and the parallelogram has a base of 5m and an altitude of 3.5m. Then, the area of the figure is:

`(3.5m*3.5m)+(5m*3.5m)=12.25m^2+17.5m^2=29.75m^2`

Then, statement C is true.

D)

Find the area of figure A by adding the area of the rectangle with base 7m and altitude 4m and the area of the two semicircles, which is the same as the area of one complete circle with radius 2m:

`(7m*4m)+(\pi*\lbrack2m\rbrack^2)=28m^2+4\pi m^2=40.56637061\ldots m^2`

Substract the area of the figure B from the figure A to find how much more is the area of figure A:

`40.56637061\ldots m^2-29.75m^2=10.81637061\ldots m^2`

Then, the area of figure A is 10.8 m^2 more than the area of figure B. The statement D is false.