Find the area of the red region

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In summary, the diagram shows a parallelogram with green regions of area 8, 10, 72, and 79 units squared. The question asks for the area of the red region, which can be calculated by subtracting the total area of the green regions from the total area of the parallelogram.
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The diagram below (which is not drawn to scale) shows a parallelogram. The area of the green regions are 8 unit² , 10 unit² , 72 unit² and 79 unit² respectively. Find the area of the red region.

[TIKZ]
\coordinate (A) at (0,0);
\coordinate (B) at (8,0);
\coordinate (C) at (12,0);
\coordinate (D) at (12.75,3);
\coordinate (E) at (14,8);
\coordinate (F) at (6,8);
\coordinate (G) at (2,8);
\coordinate[label=above: \huge 79] (P) at (4.5,3);
\coordinate[label=above: \huge 72] (Q) at (9.5,6);
\coordinate[label=above: \large 8] (R) at (8.5,1.2);
\coordinate[label=above: \large 10] (S) at (11,2.9);
\draw (A) -- (C)-- (E) -- (G) -- (A);
\draw (A) -- (F);
\draw (A) -- (D);
\draw (B) -- (F);
\draw (B) -- (E);
\draw (D) -- (G);
\draw[fill=teal] (0,0) -- (7.564,1.745) -- (6.513,5.949) -- (4.983,6.644);
\draw[fill=teal] (6,8) -- (6.508,5.931) -- (10.93,3.85) -- (14,8);
\draw[fill=teal] (8,0) -- (7.564,1.76) -- (9.674,2.25);
\draw[fill=teal] (10.92,3.89) -- (12.75,3) -- (9.674,2.25);
\draw[fill=teal] (4.5,3) node[text=pink] {\huge 79};
\draw[fill=teal] (9.5,6) node[text=pink] {\huge 72};
\draw[fill=teal] (8.5,1.2) node[text=pink] {\large 8};
\draw[fill=teal] (11,2.9) node[text=pink] {\large 10};
\draw[fill=magenta] (2,8) -- (4.983,6.644) -- (6,8);
[/TIKZ]
 
Last edited:
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Area of triangle
 
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[TIKZ]
\coordinate (A) at (0,0);
\coordinate (B) at (8,0);
\coordinate (C) at (12,0);
\coordinate (D) at (12.75,3);
\coordinate (E) at (14,8);
\coordinate (F) at (6,8);
\coordinate (G) at (2,8);
\coordinate[label=above: \huge 79] (P) at (4.5,3);
\coordinate[label=above: \huge 72] (Q) at (9.5,6);
\coordinate[label=above: \large 8] (R) at (8.5,1.2);
\coordinate[label=above: \large 10] (S) at (11,2.9);
\coordinate[label=above: \huge A] (M) at (2.5,5);
\coordinate[label=above: \huge B] (N) at (6,0.48);
\coordinate[label=above: \huge C] (Z) at (5.8,6.8);
\coordinate[label=above: \huge D] (J) at (8.5,3.2);
\coordinate[label=above: \huge E] (K) at (10.5,0.9);
\coordinate[label=above: \huge F] (I) at (12.2,4.2);
\draw (A) -- (C)-- (E) -- (G) -- (A);
\draw (A) -- (F);
\draw (A) -- (D);
\draw (B) -- (F);
\draw (B) -- (E);
\draw (D) -- (G);
\draw[fill=teal] (0,0) -- (7.564,1.745) -- (6.513,5.949) -- (4.983,6.644);
\draw[fill=teal] (6,8) -- (6.508,5.931) -- (10.93,3.85) -- (14,8);
\draw[fill=teal] (8,0) -- (7.564,1.76) -- (9.674,2.25);
\draw[fill=teal] (10.92,3.89) -- (12.75,3) -- (9.674,2.25);
\draw[fill=teal] (4.5,3) node[text=pink] {\huge 79};
\draw[fill=teal] (9.5,6) node[text=pink] {\huge 72};
\draw[fill=teal] (8.5,1.2) node[text=pink] {\large 8};
\draw[fill=teal] (11,2.9) node[text=pink] {\large 10};
\draw[fill=magenta] (2,8) -- (4.983,6.644) -- (6,8);
[/TIKZ]

If we look at the parallelogram in such a way that the horizontal sides are the base, then we have

$\normalsize \text{Area of B}+\text{Area of C}+79+\text{Area of E}+\text{Area of F}+10=\text{Area of A}+\text{Area of red region}+72+8+\text{Area of D}$

If we look at the parallelogram in such a way that the slanted sides are the base, then we have

$\normalsize \text{Area of B}+\text{Area of E}+8+\text{Area of F}+\text{Area of C}+72+\text{Area of red region}=\text{Area of A}+79+10+\text{Area of D}$

Subtracting the below from the above we get

$ 9-\text{Area of red region}=-9+\text{Area of red region}\\ \\ \therefore \text{Area of red region}=9$
 

FAQ: Find the area of the red region

1. What is the red region in "Find the area of the red region"?

The red region refers to a specific portion of a shape or area that is shaded or highlighted in red.

2. How do you calculate the area of the red region?

The area of the red region can be calculated by finding the total area of the shape or area and subtracting the area of any non-red regions within it.

3. What units are used to measure the area of the red region?

The units used to measure the area of the red region will depend on the units used to measure the overall shape or area. For example, if the shape is measured in square inches, then the area of the red region will also be in square inches.

4. Can the area of the red region be negative?

No, the area of the red region cannot be negative. It represents a physical measurement and therefore cannot have a negative value.

5. Are there any specific formulas or equations used to find the area of the red region?

The formula used to find the area of the red region will depend on the shape or area being measured. For example, the formula for finding the area of a circle is different from finding the area of a triangle. It is important to use the appropriate formula for the specific shape or area being measured.

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