Question

1. ayana wrote the expression below. does this expression represent the surface area of nina’s earring in the example? explain.

2(18·18)+2(\frac{1}{2})(18·14)+2(\frac{1}{2})(18·14)

1. what is the surface area of the right rectangular prism? show your work.

Explanation:

Step1: Recall surface - area formula for rectangular prism

The surface - area formula of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step2: Identify dimensions for the given prism

For the rectangular prism with $l = 15$ cm, $w = 10$ cm, and $h = 7$ cm.

Step3: Calculate each part of the formula

First, calculate $lw$: $lw=15\times10 = 150$ cm².
Second, calculate $lh$: $lh = 15\times7=105$ cm².
Third, calculate $wh$: $wh = 10\times7 = 70$ cm².

Step4: Calculate the surface area

$SA=2(150 + 105+70)=2\times325 = 650$ cm².

For the first question about Ayana's expression $2(18\cdot18)+2(\frac{1}{2})(18\cdot14)+2(\frac{1}{2})(18\cdot14)$:

Step1: Analyze the structure of the expression

The first term $2(18\cdot18)$ might represent the area of two square - like faces. The second and third terms $2(\frac{1}{2})(18\cdot14)$ and $2(\frac{1}{2})(18\cdot14)$ (which are the same) might represent the area of two triangular - like faces. However, if it's supposed to be a surface - area of a 3 - D shape, and assuming it's not a standard polyhedron, we need to know the shape of Nina's earring. If it's a rectangular - prism - like or other standard 3 - D shape, this expression doesn't match the standard surface - area formula for common 3 - D shapes. If it's a non - standard shape, we need more information about the earring's geometry. But if we assume it's a wrong application of surface - area formula for a standard 3 - D solid, we can say no.

Answer:

1. Without more information about Nina's earring shape, we can't be sure, but if we assume standard 3 - D shapes, the answer is no.
2. 650 cm²