Question

to find the area of a triangle, use the formula area = \\( \frac { 1 } { 2 } \\) x base x height or \\( a = \frac { 1 } { 2 } \times b \times h \\).
example:
\\( a = \frac { 1 } { 2 } \times b \times h \\)
\\( a = \frac { 1 } { 2 } \times 7 \mathrm { cm } \times 4 \mathrm { cm } \\)
base = 70 mm (7 cm)
\\( a = \frac { 1 } { 2 } \times 28 \mathrm { cm } ^ { 2 } \\)
height = 4 cm
\\( a = 14 \mathrm { cm } ^ { 2 } \\)
find the area of each triangle. some triangles have mixed units.
area =
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find the area of each triangle using the base and height measurements.
g. b = 75.33 meters h = 68 meters
h. b = 47.2 centimeters h = 595 millimeters
i. b =.875 meters h = 92 centimete

Explanation:

Step1: Convert units if necessary

For part b: \(450\ mm = 45\ cm\)
For part e: \(420\ cm = 4.2\ m\)
For part f: \(1\frac{1}{5}\ km=1200\ m\)
For part h: \(595\ mm = 59.5\ cm\)
For part i: \(92\ cm = 0.92\ m\)

Step2: Apply the formula \(A=\frac{1}{2}\times b\times h\)

Part a:

\(b = 20.2\ m\), \(h = 22.34\ m\)
\(A=\frac{1}{2}\times20.2\times22.34\)
\(A = 10.1\times22.34=225.634\ m^{2}\)

Part b:

\(b = 38.6\ cm\), \(h = 45\ cm\)
\(A=\frac{1}{2}\times38.6\times45\)
\(A = 19.3\times45 = 868.5\ cm^{2}\)

Part c:

\(b = 48.4\ cm\), \(h = 24.3\ cm\)
\(A=\frac{1}{2}\times48.4\times24.3\)
\(A = 24.2\times24.3=588.06\ cm^{2}\)

Part d:

\(b = 12.5\ mm\), \(h = 15.4\ mm\)
\(A=\frac{1}{2}\times12.5\times15.4\)
\(A = 6.25\times15.4 = 96.25\ mm^{2}\)

Part e:

\(b = 4.2\ m\), \(h = 3.75\ m\)
\(A=\frac{1}{2}\times4.2\times3.75\)
\(A = 2.1\times3.75=7.875\ m^{2}\)

Part f:

\(b = 1200\ m\), \(h = 820\ m\)
\(A=\frac{1}{2}\times1200\times820\)
\(A = 600\times820=492000\ m^{2}\)

Part g:

\(b = 75.33\ m\), \(h = 68\ m\)
\(A=\frac{1}{2}\times75.33\times68\)
\(A = 37.665\times68 = 2561.22\ m^{2}\)

Part h:

\(b = 47.2\ cm\), \(h = 59.5\ cm\)
\(A=\frac{1}{2}\times47.2\times59.5\)
\(A = 23.6\times59.5=1404.2\ cm^{2}\)

Part i:

\(b = 0.875\ m\), \(h = 0.92\ m\)
\(A=\frac{1}{2}\times0.875\times0.92\)
\(A = 0.4375\times0.92=0.4025\ m^{2}\)

Answer:

a. \(225.634\ m^{2}\)
b. \(868.5\ cm^{2}\)
c. \(588.06\ cm^{2}\)
d. \(96.25\ mm^{2}\)
e. \(7.875\ m^{2}\)
f. \(492000\ m^{2}\)
g. \(2561.22\ m^{2}\)
h. \(1404.2\ cm^{2}\)
i. \(0.4025\ m^{2}\)