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;
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
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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