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MissTica
2 years ago
8

20 points.Solve for a.​

Mathematics
2 answers:
Hoochie [10]2 years ago
4 0

Answer:

30 degrees

Step-by-step explanation:

The sum of exterior angles = 360 degree

102 + 73 + 67 + 88 + a = 360

330 + a = 360

a = 360 - 330

a = 30 degree.

HOPE THIS HELPED YOU

AlladinOne [14]2 years ago
3 0

Answer:

a = 30

Step-by-step explanation:

The total exterior angles of a pentagon is 360 degrees, meaning:

102 + 73 + 67 + 88 + a = 360

330 + a = 360

Subtract 330 from both sides:

330 + a - 330 = 360 - 330

a = 30

Hope this helps!

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The composite figure shown has a surface area of 844 square centimeters.
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Given the surface area of the composite figure, the height of the rectangular prism is approximately 8 centimeters.

<h3>What is the height of the rectangular prism?</h3>

First we calculate the surface area of the rectangular pyramid;

S.A = lw + (1/2)w√(4h²+l²) + (1/2)l√(4h²+w²)

Given that;

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  • h = 12cm

S.A = lw + (1/2)w√(4h²+l²) + (1/2)l√(4h²+w²)

S.A = (18cm×10cm) + (1/2)10cm√(4(12cm)²+18cm²) + (1/2)18cm√(4(12cm)²+(10cm)²)

S.A = (180cm²) + 5cm√(576cm² + 324cm²) + 9cm√(576² + 100cm²)

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Now, surface Area of the rectangular prism will be;

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Now surface area of rectangular prism is expressed as;

SA = 2lw + 2lh + 2hw

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  • l = 18cm
  • h = x

SA=2lw + 2lh + 2hw

SA - 2lw  =  h( 2l + 2w)

h = (SA - 2lw) / ( 2l + 2w)

h = (1280cm² - ( 2×18cm×10cm)) / ( 2×18cm + 2×10cm)

h = (1280cm² - 360cm²) / ( 36cm + 20cm)

h = 1020cm² / 56cm

h = 8cm

Given the surface area of the composite figure, the height of the rectangular prism is approximately 8 centimeters.

Learn more about Prism and Pyramid here: brainly.com/question/9796090

#SPJ1

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