Question

area of triangles directions: calculate the area of each figure. show all work. #1 15in 40in area: __ #2 6m 8m area: #3 2.8cm 5.6cm area: #4 4.5m 12m area: #5 2.7in 5.4in area: #6 21.1m 6.8m area: __

Explanation:

Step1: Recall area formula

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Solve for #1

For the first triangle with $b = 40$ in and $h=15$ in, we substitute into the formula: $A=\frac{1}{2}\times40\times15=300$ in².

Step3: Solve for #2

For the second triangle with $b = 8$ m and $h = 6$ m, $A=\frac{1}{2}\times8\times6 = 24$ m².

Step4: Solve for #3

For the third triangle with $b=5.6$ cm and $h = 2.8$ cm, $A=\frac{1}{2}\times5.6\times2.8=7.84$ cm².

Step5: Solve for #4

For the fourth triangle with $b = 4.5$ m and $h=12$ m, $A=\frac{1}{2}\times4.5\times12 = 27$ m².

Step6: Solve for #5

For the fifth triangle with $b = 5.4$ in and $h=2.7$ in, $A=\frac{1}{2}\times5.4\times2.7=7.29$ in².

Assuming the base and height for #6 are $b = 6.8$ m and $h=21.1$ m (if the given sides are base - height pair), $A=\frac{1}{2}\times6.8\times21.1=71.74$ m².

Answer:

#1: 300 in²
#2: 24 m²
#3: 7.84 cm²
#4: 27 m²
#5: 7.29 in²
#6: 71.74 m²