Final answer:
Keith used the formula for the area of a rectangle (base times height) and the area of a triangle (1/2 base times height) to find the area of each shape within the parallelogram. He then added the areas of the rectangle and the two triangles to get the total area of the parallelogram, making sure to use the correct number of significant figures.
Step-by-step explanation:
Keith determined the area of a parallelogram by decomposing it into a rectangle and two triangles. The formula to calculate the area of a rectangle is base times height (b × h). To find the area of a triangle, the formula is 1/2 times base times height (1/2 × b × h). Keith would first calculate the area of the rectangle within the parallelogram and then calculate the area of each triangle. Since triangles are identical in this decomposition method, we multiply the area of one triangle by two to get the total area for both triangles.
For example, if the rectangle had a base of a meters and a height of b meters, its area would be a × b square meters. Each triangle, with the same height b and a base of a/2 (assuming the height bisects the base), would have an area of 1/2 × (a/2) × b, or a × b/4 square meters. The total area of the parallelogram would thus be a × b + 2(× a × b/4), which simplifies to a × b + a × b/2 = 3a × b/2 square meters.
To ensure the correct number of significant figures, Keith would need to consider the precision of the measurements given for the base and height of the parallelogram. Also, when converting measurements, such as from centimeters to meters, he would use conversion factors that do not affect the determination of significant figures since they are considered exact numbers.