yards long, and the height (a perpendicular drawn from this base to the point or summit of the opposite angle) 83 yards. Multiply 77 (that is, half the base) by 83, and I have-the answer, 6391 square yards of surface.
The superficies, or surface of a polygon, or a pyra- mid, is found by taking separately the surfaces of the triangles of which they are composed.
2. An irregular court has a quadrilateral (four sided) form. To find its surface, I measure one of the diago- nals which I find to be 129,7 yards. I draw perpen- diculars from the angles opposite this diagonal, one of which I find to be 52,5 yds. and the other, 41,8 yds- i consider the court as forming two triangles, and find their superficies separately, thus :
First triangle . . 129,7 Second triangle . . 129,7 Height.....52,5 Height ...... 41,8
6485 10376
2594 1297
6485 5188
' 6809,25> 5421,46
6809,25
2) 12230,71 Square yards, .... 6115,355
But as this requires two multiplications, it is a shorter way to add the two heights, 52,5 and 41,8 which gives 94,3 of which the half, 47,15 multiplied by 129,7 the base, gives 6115,355 square yards as above.
3. A four sided polygon has a diagonal of 66 feet, 3,8 inches ; the height of one triangle is 22 feet, 6,6 inches ; and of the other, 18 feet, 8,2 inches ; requir- ed the superficial contents of the polygon.
Ans. 195880,9 inches, or 1360 square feet.
