Question

what is the area of this figure? write your answer using decimals, if necessary. square feet

Explanation:

Step1: Divide the figure into rectangles and a triangle

We can divide the given figure into 3 rectangles and 1 right - angled triangle.

Step2: Calculate the area of the first rectangle

The first rectangle has dimensions 5 ft by 4 ft. The area formula for a rectangle is $A = l\times w$. So, $A_1=5\times4 = 20$ square feet.

Step3: Calculate the area of the second rectangle

The second rectangle has dimensions 3 ft by 3 ft. Using the rectangle area formula, $A_2 = 3\times3=9$ square feet.

Step4: Calculate the area of the third rectangle

The third rectangle has dimensions 2 ft by 2 ft. So, $A_3=2\times2 = 4$ square feet.

Step5: Calculate the area of the triangle

The triangle has a base of 10 ft and a height of $(4 + 3+2)=9$ ft. The area formula for a triangle is $A=\frac{1}{2}\times b\times h$. So, $A_4=\frac{1}{2}\times10\times9=45$ square feet.

Step6: Calculate the total area of the figure

The total area $A = A_1+A_2+A_3+A_4$. Substitute the values: $A=20 + 9+4+45=78$ square feet.

Answer:

78