Question 35222
Assume that the only area formula you know is the formula for the area of a triangle. Explain how to derive the formula for the area of the trapezoid
LET ABCD BE THE TRAPEZOID WITH AB PARALLEL TO CD.SEE DIAGRAM BELOW.
FROM C AND D DRAW CF AND DE PERPENDICULARS TO AB MEETING AB AT F AND E
JOIN EC
NOW AREA OF TRAPEZIUM =AREA OF TRIANGLE ADE+AREA OF TRIANGLE DEC+AREA OF TRIANGLE EFC+TRIANGLE CFB....ALL ARE RIGHT ANGLED TRIANGLES HENCE AREA =BASE*HT/2..HT.FOR ALL TRIANGLES =H=DE=CF=DISTANCE BETWEN PARALLEL SIDES OF TRAPEZIUM
AREA=(1/2)*H{AE+DC+EF+FB)=(1/2)*H(AE+EF+FB+DC)=(1/2)*H(AB+DC)
AREA OF TRAPEZIUM =(1/2)(SUM OF PARALLEL SIDES )(PERPENDICULAR DISTANCE BETWEEN THE 2 PARALLEL SIDES)
{{{drawing(600,600,-5,20,-5,20,red( line( 0,0, 16,0 ) ),locate( 0, 0, A ),red( line( 16,0,12,10 ) ),locate( 16,0, B ),locate( 12, 10, C ),red( line( 12,10,4,10 ) ),locate( 4,10, D ),locate( 4, 0, E),locate(12,0,F),red(line(0,0,4,10)),red(line(4,10,4,0)),red(line(12,0,12,10)),red(line(4,0,12,10)))}}}