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CHAPTER VII-MEASUREMENT OF AREAS.
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of this derived longish quadrilateral figure), gives rise to the measure of the top-side. The value of the perpendicular-side of he derived longish quadrilateral figure), on being multiplied by mo and increased by the value of the top-side (already arrivod it), gives rise to the value of the base. The value of the baso (of he derived longish quadrilateral figuro) is (the same as that
1 %
The first thing we have to do is to constrnot a rectangle with the aid of ho given bijas in accordance with he rule laid down in Atanza 904 in his chapter. That rectangle oomos o have 6 for the mensure of its imaller side, 12 for the measure of ts larger side, and 13 for the neagre of its diagonal; and its irea is 60 in value. Now the aren given in the problem is to be multiplied by the square of the given yptional nunbor in the problein, so that we obtain 7 x3 = 63. Frourth is 03, We have to subtract 60, which is
he measure of the area of the rectangle oonstructed on the bnais of the given bijn: and this gives 3
12 18 the remainder. Then the thing to be done is to construct a rectangle, the iron whereof is equal to this 8, and one of the sides is equal to the longer side of the rectangle derived from the same bijas. Binoe this longer vide is equal to 12 in valile, the smaller side of the required reotangle has to be in value as shown in the figure here. Then the two triangles, into which the rectangle derived from the bijas may be split up by its diagonal are added one un each sido to this last rectangle, so that the sides measuring 12 in the case of these triangles coincido with the sides of the rectangle having 12 as their measure. The figure here exbibits the operation.
Thus in the end we get the quadrilateral figare having two equal wider, each of which measures 18, the value of the other two sides being + and 10% respectively. From this the values of the sides of the quadrilateral required in the problem may be obtained by dividing hy the given Optional namaber damely 3, the values of its sides reprosettod by 13, , 18 and 101
