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Dmitry_Shevchenko [17]
2 years ago
13

An isosceles trapezoid has base angles equal to 45 and bases of lengths 6 and 12. Find the area of the trapezoid.

Mathematics
2 answers:
swat322 years ago
8 0

Answer:

First option: 27 square units.

Step-by-step explanation:

The formula for calculate the area of a trapezoid is:

A=\frac{h}{2}(B+b)

Where h is the height, B the larger base and b the smaller base.

Observe the figure of the trapezoid called ABCD. The length of the larger base (AB) is 12 units and the lenght of the smaller base (CD) is 6 units, but the height h is unknown, so you need to find it.

You can observe in the figure that two equal right triangles are formed, whose opposite side is the height "h". If you calculate the opposite side of one of those triangles, you will  obtain the height of the trapezoid.

For this, you can use the identity tan\alpha=\frac{opposite}{adjacent}.

Identify the opposite side, the adjacent side and the angle \alpha:

opposite=h\\adjacent=\frac{12units-6units}{2}=3units\\\alpha=45\°

Substitute and solve for the height h:

tan(45\°)=\frac{h}{3}\\(3)(tan(45\°)=h\\3units=h

Finally substitute into A=\frac{h}{2}(B+b):

A=\frac{3units}{2}(12units+6units)=27units^2

Natali [406]2 years ago
8 0

Answer:

27 sq. units

Step-by-step explanation:

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The diameter of a large sphere is 4 times the diameter of a small sphere. The surface area of the large sphere is how many times
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Surface Area of a Sphere = 4π(d/2)²
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QUESTION 2. the feasible region shows the number of chairs x and tables y that a furniture company can build each week.
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Answer:

Part a) The company can not build 12 chairs and 5 tables

Part b) The company can build 18 chairs and 3 tables

Part c) The company  can build 12,13,14,15,16 or 17 chairs

Step-by-step explanation:

we know that

If a ordered pair is a solution, then the ordered pair must be belong to the feasible region of the graph

Part a) Can the company build 12 chairs and 5 tables?

In this problem we have the ordered pair A(12,5)

Plot  and verify if the point belong to the feasible region of the graph

see the attached figure to better understand the problem

The point A is not on the feasible region

therefore

The company can not build 12 chairs and 5 tables

Part b) Can the company build 18 chairs and 3 tables?

In this problem we have the ordered pair B(18,3)

Plot  and verify if the point belong to the feasible region of the graph

see the attached figure to better understand the problem

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therefore

The company can build 18 chairs and 3 tables

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For y=4

Find the value of x in the graph

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therefore

The company  can build 12,13,14,15,16 or 17 chairs

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