randRange(2, 8)
randRange(2, 8)
randRange(1, 6)
randRangeNonZero(-2, 2)
1/2 * (B1 + B2) * H
What is the area of this figure?
init({
range: [[-4, max(B1, B2) + 4], [-1, H + 1]],
scale: [30, 30]
});
style({ stroke: BLUE, fill: "#eee"});
path([[0, 0], [B1, 0], [B2 + SH, H], [SH, H], [0, 0]]);
label([B1/2, 0], B1 + "\\text{ " + UNIT + "}", "below");
label([B2/2 + SH, H], B2 + "\\text{ " + UNIT + "}", "above");
var x = min(B1, B2 + SH);
line([x, 0], [x, H], { strokeDasharray: "." });
label([x, H/2], H + "\\text{ " + UNIT + "}", "right");
rightAngleBox([[0, 0], [x, 0]], [[x, 0], [x, H]], { stroke: GRAY, opacity: 0.5 });
parallel([[0, 0], [B1, 0]], 1);
parallel([[SH, H], [B2 + SH, H]], 1);
K
square plural_form(UNIT_TEXT)
This figure is a quadrilateral with a pair of parallel sides (the top and bottom sides), so it's a trapezoid.
area of a trapezoid = \dfrac12 \cdot (b_1 + b_2) \cdot h
[Show me why]
Let's draw a line between the opposite ends of the two bases.
var showSubHint = function() {
graph.subhint.show();
$("a[data-subhint='area-trapezoid']")
.unbind("click", showSubHint)
.click(hideSubHint);
};
var hideSubHint = function() {
graph.subhint.hide();
$("a[data-subhint='area-trapezoid']")
.unbind("click", hideSubHint)
.click(showSubHint);
};
graph.subhint = raphael.set().push(
path([[0, 0], [B1, 0], [B2 + SH, H]], { stroke: BLUE, fill: ORANGE, opacity: 0.5 }),
path([[SH, H], [B2 + SH, H], [0, 0]], { stroke: BLUE, fill: RED, opacity: 0.5 })
);
hideSubHint();
Notice that the line divides the trapezoid into two triangles: one triangle with base b_1 = B1, and another triangle with base b_2 = B2. Both triangles have height h = H.
The area of the trapezoid is equal to the sum of the areas of the two triangles.
A = \dfrac12 \cdot b_1 \cdot h + \dfrac12 \cdot b_2 \cdot h
Factor out \dfrac12 \cdot h to get the formula for the area of a trapezoid:
A = \dfrac12 \cdot h \cdot (b_1 + b_2) = \dfrac12 \cdot (b_1 + b_2) \cdot h
Now use this formula to calculate the trapezoid's area.
b_1 = B1
b_2 = B2
h = H
A = \dfrac12 \cdot (B1 + B2) \cdot H = K