Areas Research Paper Example | Topics and Well Written Essays - 500 words

Areas - Research Paper Example Therefore, the total number of square units in the rectangle will be ‘b times h’, which is the area of the rectangle. Thus, the area of a reachable is given by: The line DC is extended to point F. The line AE is perpendicular on the line DC and the line BF is perpendicular on the line DF. The shape (triangle) represented by enclosures ADE and BCF are same (congruent triangles). Therefore, if we cut part ADE from the parallelogram from left and place this to the right on part BCF, than the enclosure ABFE will be a rectangle with base b and height h. Therefore, the area of the parallelogram ABCD will be equal to the area of the rectangle ABFE that is given by: The line DA is parallel to line BC and the line DB is parallel to the line AC. The enclosure DACB represents a parallelogram with base b and height h. The line AB divides the parallelogram DACB into two congruent triangles. Therefore, the area of the triangle ABC will be half the area of the parallelogram DACB, which is given by: Figure 5 shows a trapezoid (enclosure EFGH) with bases b1 and b2, and height h. This trapezoid can be separated in two triangles, triangle FGH and triangle FEH. Thus, the area of the trapezoid will be sum of these two triangles. The triangle FGH with base b1 and height h. and the triangle FEH with base b2 and height h. The circumference C of a circle is equal to its diameter d times π, or 2 times its radius r times π. Finding the area of a circle is related to finding the area of a parallelogram. A circle can be separated into congruent wedge-like pieces, as shown in figure 6 (left). These wedge-like pieces can be arranged to form a figure similar to a parallelogram as shown in figure 6 (right). Thus, the circle has an area that is relatively close to the area of the parallelogram-shaped figure. Therefore, we can use the formula for the area of a parallelogram to find the area of a circle. In