Calculate the Area of a Modified Rectangle: 6cm × 7cm with Erased Segment

Question

The shape below consists of a rectangle from which the line segment BH has been erased.

AB = 6 cm

AH = 7 cm

EF = 3 cm

HG = 12 cm

BC = 3 cm

Calculate the area of the shape shaded orange.

Video Solution

Solution Steps

00:00 Calculate the area of the brown shape

00:03 First calculate the area of the triangle ABC

00:06 (height(7) x base(6)) divided by 2

00:10 This is the area of the triangle ABC

00:15 Apply the same method and formula in order to calculate the area of the triangle HGD

00:23 This is the area of the triangle HGD

00:30 Complete BH into a square

00:37 Calculate its area by side(3) squared

00:40 This is the area of the square BHFE

00:45 Calculate the area of the large rectangle AGDC

00:49 side(12) multiplied by side(7)

00:52 This is the area of the rectangle AGDC

00:57 To calculate the area of the brown shape, we need to subtract areas

01:01 We'll subtract the areas of the triangles and the square from the area of the large rectangle

01:09 This is the solution

Step-by-Step Solution

Let's first calculate the area of triangle ABC:

$\frac{6\times7}{2}=\frac{42}{2}=21$

Since the shape before us is a rectangle, we can claim that:

AC=GD=7

Now let's calculate the area of triangle HGD:

$\frac{7\times3}{2}=\frac{21}{2}=10.5$

Let's draw an imaginary line between B and H to get square BEFH where each side equals 3 cm.

Let's calculate the area of BEFH:

$3\times3=9$

Let's calculate the area of rectangle ACDG:

$7\times12=84$

Now we can calculate the area of the brown shape by subtracting the other areas we found:

Answer

43.5 cm

Related Subjects

The Area of a Triangle Calculating the Area of a Rectangle Area Area of Equilateral Triangles Area of a Scalene Triangle Area of Isosceles Triangles Rectangle Triangle Area of a right triangle Areas of Polygons for 7th Grade How do we calculate the area of complex shapes? How to calculate the area of a triangle using trigonometry?

Question Types

Area of a Rectangle: Subtraction or addition to a larger shape Area of a Triangle: Subtraction or addition to a larger shape