Page 18 - How To Solve Word Problems In Calculus

Two–Dimensional Geometry Problems
Most geometry problems are composed of rectangles, trian-
gles, and circles. It is therefore useful to review the formulas
for the perimeter and area of these standard geometric shapes.
A rectangle of length l and width w has a perimeter equal
to the sum of the lengths of its four sides. Its area is the product
of its length and width.

P = 2l + 2w
A = lw

A special case arises when l and w are equal. The resulting
figure is a square, whose side is s.

P = 4s
A = s 2

l s

w s

P = 2l + 2w P = 4s
A = lw A = s 2
1
A triangle with base b and altitude h has an area of bh.
2
Special cases include right triangles and equilateral triangles.
One often encounters triangles where two sides and their in-
cluded angle are known.

1
A = bh General formula for all triangles
2
1
A = ab Right triangle whose legs are a and b
2
√
3
A = s 2 Equilateral triangle of side s
4
1
A = ab sin θ If two sides and the included angle
2
are known

5