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Gelneren [198K]
3 years ago
5

2 Points

Mathematics
2 answers:
masya89 [10]3 years ago
6 0
The answer is 120. Because inscribed angle is Half of the arc measure. Double 60 and we get 120.
chubhunter [2.5K]3 years ago
5 0

Answer:

240

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

60 = 1/2 XZ

Multiply each side by 2

120 = XZ

But we want XYZ

XZ + XYZ = 360

120 + XYZ = 360

XYZ = 360 -120

XYZ = 240

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Surface area is just the area of all these 4 triangles plus the rectangle.

First we can find the area of the rectangle.

\sf A=lw

Half of the length is 28 cm, so the full length must be 28 * 2 = 56 cm.

\sf A=(56)(27)

\sf A=1512cm^2

The base for the left and right triangles are 27. The heights would be the net length minus half the length of the rectangle:

\sf 82.8-28=54.8\? cm

Calculate the area:

\sf A=\dfrac{1}{2}bh

\sf A=\dfrac{1}{2}(27)(54.8)

\sf A=739.8\?cm^2

We have two of these triangles.

\sf 739.8\times 2=1479.6\? cm^2

Now do the other two pair of triangles. The bases for them are 28 + 28 = 56 cm. The heights would be the net width minus the width of the rectangle:

\sf 81.2-27=54.2\?cm

Now find the area:

\sf A=\dfrac{1}{2}bh

\sf A=\dfrac{1}{2}(56)(54.2)

\sf A=1517.6\? cm^2

We have two of these triangles.

\sf 1517.6\times 2=3035.2\?cm^2

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