Mathematics for Carpenters and Builders - Carpenter's and Builder's Math, Plans, and Specifications - page 173

C C

D

AREA OF ONE
SIDE = 180 SQ FT

30 FT

A B

A

B

BASE

12 FT

(A) (B)

Figure 5-57 To find the area of a triangle (equal to 1

/ 2 area of

parallelogram ABDC).

Example How many square feet of sheathing are required to cover
a church steeple having four triangular sides?
Problem 9
To find the area of a trapezoid.
Rule: Multiply one-half the sum of the two parallel sides by the
perpendicular distance between them.
Example What is the area of the trapezoid shown in Figure 5-58?
LA and FR are the parallel sides, and MS is the perpendicular
distance between them. Therefore,
area

=

1

/ 2 ( LA

+ FR ) × MS

1

area =

/ 2 (8

+ 12) × 6 = 60 square feet

Problem 10
To find the area of a trapezium.
Rule: Draw a diagonal, dividing the figure into triangles. Measure
the diagonal and the altitudes, and find the area of the triangles. The
sum of these areas is then the area of the trapezium.
Example What is the area of the trapezium shown in Figure 5-59?
(Draw diagonal LR and altitudes AM and FS. )

area of triangle ALR =

1

/ 2 (12

× 9) = 54 square feet

area of triangle LRF =

1

/ 2 (12

× 6) = 36 square feet

area of trapezium LARF = ALR + LRF = 36 + 54

= 90 square feet