# Projection Area of 3D Shapes

In this lab, you will be working on a problem involving the projection area of 3D shapes. You are given an `n x n`

`grid`

where we place some `1 x 1 x 1`

cubes that are axis-aligned with the `x`

, `y`

, and `z`

axes.

Each value `v = grid[i][j]`

represents a tower of `v`

cubes placed on top of the cell `(i, j)`

.

We view the projection of these cubes onto the `xy`

, `yz`

, and `zx`

planes.

A **projection** is like a shadow, that maps our **3-dimensional** figure to a **2-dimensional** plane. We are viewing the "shadow" when looking at the cubes from the top, the front, and the side.

Your task is to create a function that returns the total area of all three projections.

Here are a few examples to clarify the problem:

**Example 1:**

**Input:** grid = [[1,2],[3,4]]
**Output:** 17
**Explanation:** Here are the three projections ("shadows") of the shape made with each axis-aligned plane.

**Example 2:**

**Input:** grid = [[2]]
**Output:** 5

**Example 3:**

**Input:** grid = [[1,0],[0,2]]
**Output:** 8

**Constraints:**

`n == grid.length == grid[i].length`

`1 <= n <= 50`

`0 <= grid[i][j] <= 50`

To solve this lab, you need to follow the instructions and rewrite the lab material according to the rules specified above.

**Challenges:**

- Create a function and name it
`projectionArea`

. Export this function as ESM. - Write test cases for the
`projectionArea`

function to test various input cases and validate the results.

**Evaluation script:**

`1import fs from 'fs' 2import { projectionArea } from '/home/damner/code/index.js' 3 4const testlog = [] 5 6try { 7 const result = projectionArea([[1, 2], [3, 4]]) 8 if (result === 17) { 9 testlog.push({ status: 'pass' }) 10 } else { 11 throw new Error('Incorrect result for example 1') 12 } 13} catch (error) { 14 testlog.push({ status: 'error', error: error.message || 'Challenge failed' }) 15} 16 17try { 18 const result = projectionArea([[2]]) 19 if (result === 5) { 20 testlog.push({ status: 'pass' }) 21 } else { 22 throw new Error('Incorrect result for example 2') 23 } 24} catch (error) { 25 testlog.push({ status: 'error', error: error.message || 'Challenge failed' }) 26} 27 28fs.writeFileSync('/home/damner/code/.labtests/testlog.json', JSON.stringify(testlog)) 29fs.writeFileSync(process.env.UNIT_TEST_OUTPUT_FILE, JSON.stringify(testlog.map(result => result.status === 'pass')))`

Adjust the evaluation script accordingly and make sure to complete the missing parts in the lab as per the instructions and rules given. Good luck!