Area Calculations: Squares, Rectangles, and Triangles

What is the calculated area of square [ABCD] using the formula $\text{Area}[ABCD] = (AB + DC) / 2 * BC$?

What is the area of quadrilateral [AFCD]?

How is the area of [ABEF] first calculated?

Which dimensions are used in the calculation of area [ABCD] when using $AB * BE$?

What is the final area of [ABEF] as calculated?

Area of a Square and Rectangle

ABCD is a square with sides AB = BC = CD = DA = 8 cm
The side lengths are also AB = CD = 6 cm, AD = BC = 6 cm
The area of a square is found by multiplying the side length by itself (AB X BC)
The area of a square ABCD with sides of 8cm each is: (8cm + 8cm)/2 = 8 cm x 4 cm = 32 cm²
The area of a rectangle is found by multiplying the length by the width
The Area of the square [ABCD] = (AB + DC) / 2 x BC = (8 + 4)/2 x 4 = 24 cm²
Another way to calculate the area of the square ABCD is: AB x BC = 8cm x 4cm = 24cm²

Area of a Triangle

The area of a triangle is calculated by multiplying the base by half the height (base x height / 2 )
The area of a triangle [ABE] is AB X BE = 7cm x 3.5 cm = 24.5 cm²
Area (AFCD) = Area of square [ABCD] - Area[ABCF]

Area of a Trapezoid and Combined Shapes

Area(AFCD) = Area(ABCD)/2 - Area(ABCF)
(DB X AC / 2)-(FB X AC / 2)=9 x 9/2 - 6 x 9/2 = 81/2 - 54/2 = 40.5 - 27 = 13.5 cm²
Area [ABEF] = Area(ABCD) - (Area AFD + Area FCE) = 6 x 6 - ((6 x 3)/2 + (3 x 3)/2) = 36 - (18/2 + 9/2) = 36 - (9 + 4.5) = 36 - 13.5 = 22.5 cm²

This quiz explores the concepts of calculating the area of various geometric shapes, including squares, rectangles, triangles, and trapezoids. It provides examples and formulas to help understand how to determine the area using different methods and dimensions. Test your knowledge on geometry and area calculation techniques!