I am aware that a loft on a detached house needs to be 50 sq m or less to permitted development

My maths from high school and triginometry is not so great - I know that a prism volume is (height * width * depth) / 3 and I ve been trying to calculate the existing volume and the new volume to understand how much additional space I need

A neighbour has done the loft conversion as follows and he did it under permitted development so no planning but I cant understand how he could have done this and I am sure he would not have done this without paperwork

Basically he has taken a detached roof and made it hip to gable on both sides and added a full width dormer

The house is ten metres wide ten metres deep and the height from eaves to roof ridge is 2.2M

By my basic calculation just converting hip to gable results in 36 cubic metres being added and thats before the addition of the full width dormer

Cubic Volume of original roof - Its a prism right? - So current volume is 10 * 10 * 2.2 / 3

Cubic Volume of hip to gable roof excluding rear dormer - Its a triangle right? - So current volume is 10 * 10 * 2.2 / 2

Additional volume created by just doing hip to gable on both sides is (10 * 10 * 2.2 / 3) - (10 * 10 * 2.2 / 2) = 36.66 M

What am I missing? And how can a full width dormer and two hip to gables be less then 50 sq m?!

My maths from high school and triginometry is not so great - I know that a prism volume is (height * width * depth) / 3 and I ve been trying to calculate the existing volume and the new volume to understand how much additional space I need

A neighbour has done the loft conversion as follows and he did it under permitted development so no planning but I cant understand how he could have done this and I am sure he would not have done this without paperwork

Basically he has taken a detached roof and made it hip to gable on both sides and added a full width dormer

The house is ten metres wide ten metres deep and the height from eaves to roof ridge is 2.2M

By my basic calculation just converting hip to gable results in 36 cubic metres being added and thats before the addition of the full width dormer

Cubic Volume of original roof - Its a prism right? - So current volume is 10 * 10 * 2.2 / 3

Cubic Volume of hip to gable roof excluding rear dormer - Its a triangle right? - So current volume is 10 * 10 * 2.2 / 2

Additional volume created by just doing hip to gable on both sides is (10 * 10 * 2.2 / 3) - (10 * 10 * 2.2 / 2) = 36.66 M

What am I missing? And how can a full width dormer and two hip to gables be less then 50 sq m?!