Question

The composite figure shown has a surface area of 844 square centimeters.

Answer 1

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

What is the height of the rectangular prism?

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;

• w = 10cm
• l = 18cm
• 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)

S.A = (180cm²) + 5cm(30cm) + 9cm(26cm)

S.A = 180cm² + 150cm² + 234cm²

S.A = 180cm² + 150cm² + 234cm²

S.A = 564cm²

Now, surface Area of the rectangular prism will be;

= Area of composite figure - surface area of the rectangular pyramid

= 1844cm² - 564cm²

= 1280cm²

Now surface area of rectangular prism is expressed as;

SA = 2lw + 2lh + 2hw

• w = 10cm
• 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

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