Find the area of the figure. (Sides meet at right angles.)

Mathematics

1 answer:

Lerok [7]2 years ago

4 0

Answer:

90 cm^2

Step-by-step explanation:

Divide the rectangle and square into two separate figures and add them together at the end.

Top rectangle: We know that area of a rectangle is A=lw. Here, we see that w=5 cm. For the length, we add 4+5+4=13 (5 comes from the bottom square). So A=5(13)=65

Bottom square: Area of a square is A=s^2 where s=5 in this case, so A=5^2=25

Total Area: Add together two figure's area: A=65+25=90 cm^2

You might be interested in

2x + y = 8 x + y = 4 The lines whose equations are given intersect at

aalyn [17]

The lines whose equations are given intersect at. (4, 0)

7 0

3 years ago

Please help with this question.

barxatty [35]

Answer:

Step-by-step explanation:

The first thing we have to do is find the measure of angle A using the fact that the csc A = 2.5.

Csc is the inverse of sin. So we could rewrite as

$\frac{1}{sinA}=2.5$ or more easy to work with is this:

$\frac{1}{sinA} =\frac{2.5}{1}$

and cross multiply to get

2.5 sinA = 1 and

$sinA=\frac{1}{2.5}$ which simplifies to

sin A = .4

Using the 2nd and sin keys on your calculator, you'll get that the measure of angle A is 23.58 degrees.

We can find angle B now using the Triangle Angle-Sum Theorem that says that all the angles of a triangle have to add up to equal 180. Therefore,

angle B = 180 - 23.58 - 90 so

angle B = 66.42

The area of a triangle is

$A =\frac{1}{2}bh$ where h is the height of the triangle, namely side AC; and b is the base of the triangle, namely side BC. To find first the height, use the fact that angle B, the angle across from the height, is 66.42, and the hypotenuse is 3.9. Right triangle trig applies:

$sin(66.42)=\frac{h}{3.9}$ and

3.9 sin(66.42) = h so

h = 3.57

Now for the base. Use the fact that angle A, the angle across from the base, measures 23.58 degrees and the hypotenuse is 3.9. Right triangle trig again:

$sin(23.58)=\frac{b}{3.9}$ and