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HURRYYYYYY !! The rectangular prisms shown are similar.


What is the area of the base of the smaller prism, rectangle ABCD?
1.26 cm2
1.26 cm3
3.78 cm2
3.78 cm3

HURRYYYYYY The rectangular prisms shown are similar What is the area of the base of the smaller prism rectangle ABCD 126 cm2 126 cm3 378 cm2 378 cm3 class=

Respuesta :

Answer:

Option A. 1.26 cm²

Step-by-step explanation:

Since rectangular prisms are similar therefore measurements their corresponding sides will be in the same ratio.

[tex]\frac{AB}{4.2}=\frac{BC}{2.7}=\frac{2.1}{6.3}[/tex]

Now [tex]\frac{AB}{4.2}=\frac{2.1}{6.3}=\frac{1}{3}[/tex]

[tex]AB=\frac{(4.2)(1)}{3}=1.4 cm[/tex]

Similarly [tex]\frac{BC}{2.7}=\frac{1}{3}[/tex]

[tex]BC=\frac{2.7}{3}=0.9[/tex]

Now area of the base of the smaller prism ABCD = AB×BC = 1.4×0.9 = 1.26 cm²

Option A. 1.26 cm² is the correct option.

ajeigbeibraheem

The area of the base of the smaller rectangular prism ABCD is 1.26  cm².

What is the base area of a rectangular prism?

The base area of a rectangular prism is one and a half of the base multiplied by the height of the rectangular prism.

However, for similar shapes, the base angles can be determined by relating corresponding sides to each other.

From the given diagram, the area of the smaller prism can be computed as follows:

[tex]\mathbf{\dfrac{AB}{4.2} = \dfrac{BC}{2.7} = \dfrac{2.1}{6.3}}[/tex]

So, we can have:

[tex]\mathbf{\dfrac{AB}{4.2} = \dfrac{2.1}{6.3}--- (1)}[/tex]

[tex]\mathbf{ \dfrac{BC}{2.7} = \dfrac{2.1}{6.3}---(2)}[/tex]

By cross multiplying:

[tex]\mathbf{AB = \dfrac{2.1\times 4.2}{6.3}}[/tex]

AB = 1.4 cm

[tex]\mathbf{BC = \dfrac{2.1 \times 2.7}{6.3}}[/tex]

BC = 0.9 cm

Therefore, the area of the base of the smaller prism ABCD is expressed as:

AB × BC = (1.4 × 0.9)cm²

ABCD = 1.26 cm²

Learn more about the base area of a rectangular prism here:

https://brainly.com/question/25718557

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