Area or a Irapezold $$ A=\frac{1}{2}\left(b_{1}+b_{2}\right) h $$ 6.) A trapezoid has an area of 45 square centimeters. If the bases are 10 and 5

Question

UpStudy AI · Accepted Answer

To find the height $$ h $$ of the trapezoid given the area $$ A $$ and the lengths of the bases $$ b_1 $$ and $$ b_2 $$, we can use the formula for the area of a trapezoid:

$$
A = \frac{1}{2}(b_1 + b_2) h
$$

### Known Conditions:
- Area $$ A = 45 $$ square centimeters
- Base 1 $$ b_1 = 10 $$ centimeters
- Base 2 $$ b_2 = 5 $$ centimeters

### Step-by-Step Solution:

1. **Substitute the known values into the area formula:**

$$
   45 = \frac{1}{2}(10 + 5) h
   $$

2. **Calculate the sum of the bases:**

$$
   10 + 5 = 15
   $$

3. **Substitute this sum back into the equation:**

$$
   45 = \frac{1}{2}(15) h
   $$

4. **Simplify the equation:**

$$
   45 = \frac{15}{2} h
   $$

5. **Multiply both sides by 2 to eliminate the fraction:**

$$
   90 = 15h
   $$

6. **Divide both sides by 15 to solve for $$ h $$:**

$$
   h = \frac{90}{15}
   $$

7. **Calculate the height:**

$$
   h = 6
   $$

### Final Answer:
The height $$ h $$ of the trapezoid is $$ 6 $$ centimeters.
The height of the trapezoid is 6 centimeters.

Area or a Irapezold \[ A=\frac{1}{2}\left(b_{1}+b_{2}\right) h \] 6.) A trapezoid has an area of 45 square centimeters. If the bases are 10 and 5

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Geometry Questions