Determine the area of the archway with a semicircle top arch and two rectangular pillars. the lower supports are and the area of the two supports is square meters. the upper arch can be decomposed as one semicircle with radius meters minus a semicircle with radius 3 meters. the area of the archway is ( π + 24) square meters.

 The lower supports are Congruent Rectangles and the area of the two supports is 24 square meters.

The upper arch can be decomposed as one semicircle with radius 6 meters minus a semicircle with radius 3 meters.

The area of the archway is (13.5 π + 24) square meters.

Step-by-step explanation:

By the given diagram,

The area of  the archway = The area of upper support + Area of lower support.

Since, the lower support are two congruent rectangles having dimension 3 m × 4 m

Hence, The area of lower support = 3 × 4 + 3 × 4 = 12 + 12 = 24 square m.

Now, the upper support is the common the bounded area by the two concentric semi circles having radius 3 m and 6 m,

Hence, the area of the upper support = Area of semi circle having radius 6 m - Area of semi circle having radius 3 m

Thus, the area of the archway =  (13.5 π + 24) square meters

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step-by-step explanation: