Suppose the base and parallel sides of the trapezium are labelled a and b. Suppose, also, that the distance between a and b is h.
Draw a diagonal.
This will split the trapezium into one triangle whose base is the trapezium's base (a) and another upside-down triangle whose base is the trapezium's top (b).
The heights of both these triangles will be the same as the distance between the parallel sides of the trapezium (h).
The area of the first triangle is 0.5*a*h
The area of the second triangle is 0.5*b*h
So the area of the trapezium = 0.5*a*h + 0.5*b*h = 0.5*(a+b)*h
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To find the area of a composite figure consisting of a trapezoid and a triangle, you would first calculate the area of the trapezoid using the formula A = (1/2)h(b1 + b2), where h is the height of the trapezoid and b1 and b2 are the lengths of the two parallel bases. Then, you would calculate the area of the triangle using the formula A = (1/2)bh, where b is the base of the triangle and h is the height. Finally, you would add the areas of the trapezoid and the triangle together to find the total area of the composite figure.
To work out the area of a composite shape, you will have to divide it into smaller figures.
The trapezoid is a plane figure which has surface Area, but no volume but if there was a 3d figure your equation would be. The Surface Area of a trapezoid = ½(b1+b2) x h X Height of figure.
You have to cut the trapezoid into three shapes. The three shapes will be two triangles and one rectangle or square. You have to find the area of these three shapes and then add all of the three areas up to find the area of the trapezoid.
Area of a trapezoid = 0.5*(sum of parallel side)*height