$$\triangle A B C$$ is translated 6 units to the left and 1 unit up to create $$\triangle A^{\prime} B^{\prime} C^{\prime}$$. 
![](http://admin.getprephub.com/media/editor/tp3_20230125193147737909.png)
What is the area of $$\triangle A B C$$ ?


<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea wfd-invisible="true">$$\triangle A B C$$ is translated 6 units to the left and 1 unit up to create $$\triangle A^{\prime} B^{\prime} C^{\prime}$$. 
![](http://admin.getprephub.com/media/editor/tp3_20230125193147737909.png)
What is the area of $$\triangle A B C$$ ?
</textarea><math><semantics><mrow><mi mathvariant="normal">△</mi><mi>A</mi><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A B C</annotation></semantics></math>△ABC is translated 6 units to the left and 1 unit up to create <math><semantics><mrow><mi mathvariant="normal">△</mi><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><msup><mi>B</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><msup><mi>C</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A^{\prime} B^{\prime} C^{\prime}</annotation></semantics></math>△A​′​​B​′​​C​′​​. <img src="http://admin.getprephub.com/media/editor/tp3_20230125193147737909.png" alt=""> What is the area of <math><semantics><mrow><mi mathvariant="normal">△</mi><mi>A</mi><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A B C</annotation></semantics></math>△ABC ?
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea wfd-invisible="true">Since $$\triangle A B C$$ is translated 6 units to the left and 1 unit up to create $$\triangle A^{\prime} B^{\prime} C^{\prime}$$.

Comparing $$\triangle A B C$$ and $$\triangle A^{\prime} B^{\prime} C^{\prime}$$,

$$A B=A^{\prime} B^{\prime}=6.1$$ units (height),$$B C($$ Base $$)=2$$ unit

Therefore the area of $$\triangle A B C=\frac{1}{2} \times 6.1 \times 2=6.1$$ unit $$^{2}$$</textarea>Since <math><semantics><mrow><mi mathvariant="normal">△</mi><mi>A</mi><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A B C</annotation></semantics></math>△ABC is translated 6 units to the left and 1 unit up to create <math><semantics><mrow><mi mathvariant="normal">△</mi><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><msup><mi>B</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><msup><mi>C</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A^{\prime} B^{\prime} C^{\prime}</annotation></semantics></math>△A​′​​B​′​​C​′​​.
Comparing <math><semantics><mrow><mi mathvariant="normal">△</mi><mi>A</mi><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A B C</annotation></semantics></math>△ABC and <math><semantics><mrow><mi mathvariant="normal">△</mi><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><msup><mi>B</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><msup><mi>C</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A^{\prime} B^{\prime} C^{\prime}</annotation></semantics></math>△A​′​​B​′​​C​′​​,
<math><semantics><mrow><mi>A</mi><mi>B</mi><mo>=</mo><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><msup><mi>B</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup><mo>=</mo><mn>6</mn><mi mathvariant="normal">.</mi><mn>1</mn></mrow><annotation encoding="application/x-tex" wfd-invisible="true">A B=A^{\prime} B^{\prime}=6.1</annotation></semantics></math>AB=A​′​​B​′​​=6.1 units (height),<math><semantics><mrow><mi>B</mi><mi>C</mi><mo>(</mo></mrow><annotation encoding="application/x-tex" wfd-invisible="true">B C(</annotation></semantics></math>BC( Base <math><semantics><mrow><mo>)</mo><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex" wfd-invisible="true">)=2</annotation></semantics></math>)=2 unit
Therefore the area of <math><semantics><mrow><mi mathvariant="normal">△</mi><mi>A</mi><mi>B</mi><mi>C</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mn>6</mn><mi mathvariant="normal">.</mi><mn>1</mn><mo>×</mo><mn>2</mn><mo>=</mo><mn>6</mn><mi mathvariant="normal">.</mi><mn>1</mn></mrow><annotation encoding="application/x-tex" wfd-invisible="true">\triangle A B C=\frac{1}{2} \times 6.1 \times 2=6.1</annotation></semantics></math>△ABC=​2​​1​​×6.1×2=6.1 unit <math><semantics><mrow><msup><mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex" wfd-invisible="true">^{2}</annotation></semantics></math>​2​​
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