# Compound H Shapes. Calculating the area of this H shape by splitting it up into 3 rectangles.

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.

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. This can be done 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 it’s 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.

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