Find the area of the trapezoid by decomposing it into other shapes.
A) 52 cm2
B) 58 cm2
C) 64 cm2
D) 68 cm2
Ok give a description and I can help.
hint: It will be either
a rectangle and two triangles
or
a rectangle and one triangle
I need help ASAP
To find the area of the trapezoid by decomposing it into other shapes, we will use the method of dividing the trapezoid into a rectangle and a triangle.
Here's an easy step-by-step guide to find the area:
Step 1: Identify the trapezoid's bases.
The bases of a trapezoid are the parallel sides. Let's call the longer base "a" and the shorter base "b."
Step 2: Measure the height of the trapezoid.
The height of a trapezoid is the perpendicular distance between the bases. Let's call the height "h."
Step 3: Calculate the area of the rectangle.
The rectangle will have one side equal to the base "a" and the other side equal to the height "h." So, the area of the rectangle is given by:
Rectangle area = a * h.
Step 4: Calculate the area of the triangle.
The triangle will have base equal to the difference between the two bases (a - b) and the height "h." So, the area of the triangle is given by:
Triangle area = (1/2) * (a - b) * h.
Step 5: Find the total area of the trapezoid.
Add the area of the rectangle and the area of the triangle to get the total area of the trapezoid:
Total area = Rectangle area + Triangle area.
Now, using the values provided, we can calculate the total area of the trapezoid.
Given:
a = 13 cm
b = 9 cm
h = 4 cm
Step 1: Identify the bases:
a = 13 cm (longer base)
b = 9 cm (shorter base)
Step 2: Measure the height:
h = 4 cm
Step 3: Calculate the area of the rectangle:
Rectangle area = a * h
Rectangle area = 13 cm * 4 cm = 52 cm²
Step 4: Calculate the area of the triangle:
Triangle area = (1/2) * (a - b) * h
Triangle area = (1/2) * (13 cm - 9 cm) * 4 cm = 8 cm²
Step 5: Find the total area of the trapezoid:
Total area = Rectangle area + Triangle area
Total area = 52 cm² + 8 cm² = 60 cm²
So, the correct answer is not provided in the given options.