GED Math - Area of a Triangle

Determine the area of the triangle if the base is 12 and the height is 20.

Explanation

Write the formula for the area of a triangle.

$A=\frac{BH}{2}$

Substitute the base and height into the equation.

$A=\frac{(12)(20)}{2} = 6(20) =120$

The answer is:

Find the area of a triangle with a base length of 6 and a height of $\frac{1}{4}$ .

$\frac{3}{4}$

$\frac{3}{2}$

$\frac{1}{2}$

$\frac{2}{3}$

Explanation

Write the area for a triangle.

$A = \frac{BH}{2}$

Substitute the base and height into the equation.

$A = \frac{6(\frac{1}{4})}{2} = 3(\frac{1}{4}) = \frac{3}{4}$

The answer is: $\frac{3}{4}$

If the height of a triangle is twice the length of the base, and the base length is 3.5 inches, what is the area of the triangle?

$12.25 in^{2}$

$24.5in^{2}$

$6.125in^{2}$

$15in^{2}$

Explanation

First we need to know that the formula for area of a triangle:

$Area= \frac{1}{2}(Base\cdot Height)$

We know that our base is 3.5 inches, and our height is twice that, which is 7 in.

Now we can plug in our base and height to the equation

$Area=\frac{1}{2}(3.5 in\cdot 7 in)$

Multiply and solve

$Area=\frac{1}{2}(24.5in^{2})$

$Area=12.25in^{2}$

You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, how much area will the garden take up?

Explanation

You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, how much area will the garden take up?

To find the area of a triangle, use the following formula.

$A=\frac{1}{2}bh$

Note that in a right triangle, our two arms correspond to our base and our height. Furthermore, it does not matter which is which, because when we multiply, order does not matter.

So, to find our area, simply plug in and simplify.

$A=\frac{1}{2}(6ft)(8ft)=\frac{1}{2}(48ft^2)=24ft^2$

So, our answer is 24 ft squared

Triangle

Note: Figure NOT drawn to scale.

Refer to the figure above. Give the area of the blue triangle.

Explanation

The inscribed rectangle is a 20 by 20 square. Since opposite sides of the square are parallel, the corresponding angles of the two smaller right triangles are congruent; therefore, the two triangles are similar and, by definition, their sides are in proportion.

The small top triangle has legs 10 and 20; the blue triangle has legs 20 and , where can be calculated with the following proportion:

$\frac{N}{20} = \frac{20}{10 }$

$10 N = 20 \cdot 20$

$N = 400 \div 10 = 40$

The legs of the blue triangle are 20 and 40; half their product is the area:

$\frac{1}{2} \times 20 \times 40 = 400$

Find the area of a triangle with a height of 40 and a base of 20.

Explanation

Write the formula for the area of a triangle.

$A= \frac{bh}{2}$

Substitute the base and height into the equation.

$A= \frac{20(40)}{2} = \frac{800}{2} = 400$

The answer is:

Find the area of a triangle with a base of 6cm and a height that is three times the base.

$54\text{cm}^2$

$108\text{cm}^2$

$18\text{cm}^2$

$36\text{cm}^2$

$48\text{cm}^2$

Explanation

To find the area of a triangle, we will use the following formula:

$A = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 6cm. We also know the height is three times the base. Therefore, the height is 18cm. So, we substitute. We get

$A = \frac{1}{2} \cdot 6\text{cm} \cdot 18\text{cm}$