Calculating the Area of Compound H-Shapes

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Compound H-Shapes

A compound H-shape is made up of 3 rectangles. Make sure you can work out the area of an L-shape first before you attempt this one. If you are finding the area of a compound H-shape, all you need to do is split the H-shape up into 3 rectangles and work out the area of each rectangle.

Do this by multiplying together the side lengths of each rectangle. Once the area of each rectangle is found you can sum these up to give the total area of the H-shape. If some of the sides of the H-shape are missing then you need to work these out before you start calculating the areas of the 3 rectangles.

Example:

Work out the area of this H-shaped polygon.

How to Solve: Step-by-Step Instructions

First, divide the shape up into 3 rectangles. Label the rectangles 1, 2, and 3 so the marker knows which areas you are calculating.

Also, the width of the second rectangle is missing. We can calculate the width by subtracting the 4m and 5m heights from the 12m height:

12 – 4 – 5 = 3 m

So the width of rectangle 2 is 3 m.

Now the area of rectangle 1 can be found by multiplying its two side lengths together. The length of rectangle 1 is 12m and the width is 4m:

Area of rectangle 1 = 12 × 4 = 48m²

Next, work out the area of rectangle 2 in a similar way. The length of rectangle 2 is 5m and the width is 3m:

Area of rectangle 2 = 5 × 3 = 15 m².

Finally, work out the area of rectangle 3. The length of rectangle 3 is 12m and the width is 3m:

Area of rectangle 3 = 12 ×3 = 36 m².

Since you have now worked out the area of the 3 rectangles, the total area can be found by summing up these three answers:

48 + 15 + 36 = 99m².

Therefore, the total area of the H shape is 99 square metres.

If you are asked to work out the perimeter of the H-shape, all you need to do is sum up all the side lengths. Just make sure all the lengths have been included in your total:

4 + 4 + 5 + 4 + 3 + 12 + 3 + 5 + 5 + 5 + 4 + 12 = 66m

So the perimeter of this H shape is 66m.

Make sure you look at my other math pages if you want more help on calculating areas of shapes.

Question: How do you find the area of an H shape?

Answer: This can be done is a similar way to the L shape, but split the H shape into 3 rectangles instead of 2.

Then, work out the area of the rectangles that you have made, and add up these answers.

Question: How do you find the area of a T shape?

Answer: You can split a T shape into two rectangles using a horizontal line.

Then work out the area of the two rectangles and add them together.