Question

for problems 9 - 14, find the area of the shapes.

1. area =
2. area =
3. area =
4. area =
5. area =
6. area =

Explanation:

Step1: Calculate the area of the triangle (Problem 9)

The formula for the area of a triangle is \( A=\frac{1}{2}\times base\times height \). Here, the base \( b = 10\) ft and the height \( h=7\) ft.

$$ A=\frac{1}{2}\times10\times7 = 35\ \text{ft}^2 $$

Step2: Calculate the area of the rectangle (Problem 10)

The formula for the area of a rectangle is \( A = length\times width \). Here, length \( l = 15\) yd and width \( w = 7\) yd.

$$ A=15\times7=105\ \text{yd}^2 $$

Step3: Calculate the area of the parallelogram (Problem 11)

The formula for the area of a parallelogram is \( A = base\times height \). Here, base \( b = 10\) m and height \( h = 5\) m.

$$ A=10\times5 = 50\ \text{m}^2 $$

Step4: Calculate the area of the trapezoid (Problem 12)

The formula for the area of a trapezoid is \( A=\frac{1}{2}\times h\times(b_1 + b_2)\). Here, \( h = 3\) in, \( b_1=8\) in, \( b_2 = 6\) in.

$$ A=\frac{1}{2}\times3\times(8 + 6)=\frac{1}{2}\times3\times14=21\ \text{in}^2 $$

Step5: Calculate the area of the circle (Problem 13)

The formula for the area of a circle is \( A=\pi r^2\). Here, radius \( r = 6\) ft. Taking \(\pi\approx3.14\)

$$ A=3.14\times6^2=3.14\times36 = 113.04\ \text{ft}^2 $$

Step6: Calculate the area of the square (Problem 14)

The formula for the area of a square is \( A = side\times side\). Here, side \( s=3\) in.

$$ A=3\times3=9\ \text{in}^2 $$

Answer:

1. \( 35\ \text{ft}^2\)
2. \( 105\ \text{yd}^2\)
3. \( 50\ \text{m}^2\)
4. \( 21\ \text{in}^2\)
5. \( 113.04\ \text{ft}^2\)
6. \( 9\ \text{in}^2\)