Question

find the area of each triangle.
1.
10 cm
7 cm
10 cm
a = 10×7 = 70cm²
2.
12 m
5 m
10 m
3.
15 in.
9 in.
a=\frac{15×9}{2}
a=\frac{135}{2}
a = 67.5in²
4.
13 m
7 m
find the length of each base. the area is given.
5.
a = 200 m²
16 m
6.
a = 84 in²
8 in.

Explanation:

Step1: Recall area formula

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

Step2: Solve for problem 1

Given $b = 10$ cm and $h=7$ cm, $A=\frac{1}{2}\times10\times7 = 35$ cm$^{2}$.

Step3: Solve for problem 2

Given $b = 12$ ft and $h = 5$ ft, $A=\frac{1}{2}\times12\times5=30$ ft$^{2}$.

Step4: Solve for problem 3

Given $b = 15$ in and $h = 9$ in, $A=\frac{1}{2}\times15\times9=\frac{135}{2}=67.5$ in$^{2}$.

Step5: Solve for problem 4

Given $b = 13$ m and $h = 7$ m, $A=\frac{1}{2}\times13\times7=\frac{91}{2}=45.5$ m$^{2}$.

Step6: Solve for problem 5

Given $A = 200$ m$^{2}$ and $h = 16$ m. Using $A=\frac{1}{2}bh$, we can solve for $b$. Rearranging the formula gives $b=\frac{2A}{h}$. Substituting values, $b=\frac{2\times200}{16}=25$ m.

Step7: Solve for problem 6

Given $A = 84$ in$^{2}$ and $h = 8$ in. Using $b=\frac{2A}{h}$, we substitute values: $b=\frac{2\times84}{8}=21$ in.

Answer:

1. $35$ cm$^{2}$
2. $30$ ft$^{2}$
3. $67.5$ in$^{2}$
4. $45.5$ m$^{2}$
5. $25$ m
6. $21$ in